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Transcript of Momento telefonica

  • Grafeno: a folha mais fina do mundo

    Tatiana G. RappoportInstituto de Fsica - UFRJhttp://tinyurl.com/[email protected]

    1

    1Wednesday, January 19, 2011

    http://tinyurl.com/rappoporthttp://tinyurl.com/rappoport

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    O que ?Porque os fsicos se

    interessam tanto

    Para que serve?

    Grafeno

    2

    2Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Outubro de 2010

    3

    3Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Outubro de 2010

    3

    Big Bang Theory S3E1402/10

    The EinsteinApproximation

    3Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Outubro de 2010

    3

    3Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Mas nossa estria comea em 2000...Andre Geim ganhava o Ig Nobel de Fsica por levitar um sapo

    4

    4Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Mas nossa estria comea em 2000...Andre Geim ganhava o Ig Nobel de Fsica por levitar um sapo

    4

    4Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Mas nossa estria comea em 2000...Andre Geim ganhava o Ig Nobel de Fsica por levitar um sapo

    4

    4Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Mas nossa estria comea em 2000...Andre Geim ganhava o Ig Nobel de Fsica por levitar um sapo

    4

    4Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Experimentos de 6a noite

    5

    Experimentos simples, novos e sem compromisso em reas de pesquisa diferentes da que normalmente trabalhamos

    5Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Experimentos de 6a noite

    5

    Experimentos simples, novos e sem compromisso em reas de pesquisa diferentes da que normalmente trabalhamos

    2002-E o grafite? Conhecemos h tantos anos mas no sabemos nada sobre camadas bem finas desse material

    5Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Como obter folhas finas de grafite?

    Em vez de tentar fabricar folhas finas, arrancar folhas finas de um pedao de grafite

    6

    6Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    O que so grafite e grafeno?

    7

    Cristais feitos de tomos de Carbono

    Grafite

    7Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    O que so grafite e grafeno?

    7

    Cristais feitos de tomos de Carbono

    Grafite

    Grafeno: uma nica folha

    7Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Escala e visibilidade

    8

    1m

    1mm

    1m

    1nm

    -Eu 1,62 m

    -Formiga ~5 mm

    -cabelo ~100 m

    -DNA ~2 nm

    -molcula de gua ~0.3 nm

    OH

    MO

    ME

    8Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Escala e visibilidade

    8

    1m

    1mm

    1m

    1nm

    1mm= 10-3m

    1m= 10-6m

    1mm= 10-9m

    -Eu 1,62 m

    -Formiga ~5 mm

    -cabelo ~100 m

    -DNA ~2 nm

    -molcula de gua ~0.3 nm

    OH

    MO

    ME

    8Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Do grafite pro grafeno: mtodo do durex

    9

    9Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Do grafite pro grafeno: mtodo do durex

    9

    Ozyilmaz' Group, Graphene Research, National University of Singapore

    9Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Do grafite para o grafeno

    10

    10Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Do grafite para o grafeno

    10

    10Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Do grafite para o grafeno

    10

    0.1 mm

    10Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Sobre xido de silcio

    Espessura relacionada cor

    11

    0.1 mm

    microscpio tico

    1-5 camadas

    100 camadas

    10-30 camadas

    Imagem Grupo de Manchester

    11Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Achando o grafeno

    12

    0.1 mm

    1 m = 0.001 mm

    1 m

    2004

    12Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Grafeno em detalhes

    13

    2 m

    Microscpio tico

    13Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Grafeno em detalhes

    13

    2 m

    Microscpio tico

    2 m

    Microscpio eletrnico de varredura

    13Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Grafeno em detalhes

    13

    2 m

    Microscpio tico

    2 m

    Microscpio eletrnico de varredura

    !

    "#$%&!!'()*#'+,)!!-.#/01#&)!2343!

    !

    !"#$%&'()*+,+%-,%&'()*./+%

    -200 -100 0 100 2000.0

    0.2

    0.4

    0.6

    0.8

    Sample bias (mV)

    0.0 T

    dI/dV

    (a.u

    .)

    topography B=0 spectroscopy B>0 spectroscopy

    skip

    Landau levels Linear DOS

    1 nm1nm= 0.001m

    Microscpio eletrnico de tunelamento

    13Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Grafeno em detalhes

    13

    2 m

    Microscpio tico

    2 m

    Microscpio eletrnico de varredura

    !

    "#$%&!!'()*#'+,)!!-.#/01#&)!2343!

    !

    !"#$%&'()*+,+%-,%&'()*./+%

    -200 -100 0 100 2000.0

    0.2

    0.4

    0.6

    0.8

    Sample bias (mV)

    0.0 T

    dI/dV

    (a.u

    .)

    topography B=0 spectroscopy B>0 spectroscopy

    skip

    Landau levels Linear DOS

    1 nm1nm= 0.001m

    !

    "#$%&!!'()*#'+,)!!-.#/01#&)!2343!

    !

    !"#$%&'()*+,+%-,%&'()*./+%

    -200 -100 0 100 2000.0

    0.2

    0.4

    0.6

    0.8

    Sample bias (mV)

    0.0 T

    dI/dV

    (a.u

    .)

    topography B=0 spectroscopy B>0 spectroscopy

    skip

    Landau levels Linear DOS

    Microscpio eletrnico de tunelamento

    Imagem Grupo de Rutgers

    13Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Outras formas

    14

    Grafeno

    14Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Outras formas

    14

    Fulereno

    R.F. Curl, H.W. Kroto, R. E Smalley 1985Prmio Nobel 1996

    Grafeno

    14Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Outras formas

    14

    Fulereno

    R.F. Curl, H.W. Kroto, R. E Smalley 1985Prmio Nobel 1996

    Nanotubo

    Sumio Iijima 1991

    Grafeno

    14Wednesday, January 19, 2011

    http://en.wikipedia.org/wiki/Sumio_Iijimahttp://en.wikipedia.org/wiki/Sumio_Iijima

  • Mas por que os fsicos se interessaram tanto?

    15

    15Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport 16

    Propriedades fsicas muito interessantes

    O que medir? Como medir?

    16Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport 16

    Propriedades fsicas muito interessantes

    O que medir? Como medir?

    preciso nanotecnologia

    16Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport 16

    Propriedades fsicas muito interessantes

    O que medir? Como medir?

    Propriedades eltricas

    preciso nanotecnologia

    16Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo os contatos eltricos

    Imagem de microscpio eletrnico de varredura (MEV)

    17

    2 m

    17Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo os contatos eltricos

    Imagem de microscpio eletrnico de varredura (MEV)

    Design

    18

    2 m

    18Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo os contatos eltricos

    Imagem de microscpio eletrnico de varredura (MEV)

    Design

    Dispositivo

    19

    2 m

    19Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Dispositivo

    20

    contatos de Ouro

    SiO2Si

    grafeno

    20Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Eltrons no grafeno

    21

    21Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Eltrons no grafeno

    Grafeno conduz muito bem (como um metal)

    21

    21Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Eltrons no grafeno

    Grafeno conduz muito bem (como um metal)

    Mas cargas podem ser controladas como num semicondutor

    21

    21Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Eltrons no grafeno

    Grafeno conduz muito bem (como um metal)

    Mas cargas podem ser controladas como num semicondutor

    Mobilidade recorde de 1000000 cm2/(Vs) em grafeno suspenso a baixa temperatura

    21

    21Wednesday, January 19, 2011

    http://en.wikipedia.org/wiki/Square_centimetrehttp://en.wikipedia.org/wiki/Square_centimetrehttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Second

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Eltrons no grafeno

    Grafeno conduz muito bem (como um metal)

    Mas cargas podem ser controladas como num semicondutor

    Mobilidade recorde de 1000000 cm2/(Vs) em grafeno suspenso a baixa temperatura

    Mobilidade de 50000 cm2/(Vs) a temperatura ambiente

    21

    Maior que em qualquer semicondutor

    Si: < 2000 cm2/(Vs)

    21Wednesday, January 19, 2011

    http://en.wikipedia.org/wiki/Square_centimetrehttp://en.wikipedia.org/wiki/Square_centimetrehttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Square_centimetrehttp://en.wikipedia.org/wiki/Square_centimetrehttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Square_centimetrehttp://en.wikipedia.org/wiki/Square_centimetrehttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Volthttp://en.wikipedia.org/wiki/Secondhttp://en.wikipedia.org/wiki/Second

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Eltrons no grafeno

    22

    22Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Eltrons no grafeno

    Em materiais, eltrons podem se comportar como se tivessem massa maior ou menor do que a que eles tem quando livres

    22

    22Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Eltrons no grafeno

    Em materiais, eltrons podem se comportar como se tivessem massa maior ou menor do que a que eles tem quando livres

    No grafeno, eles se comportam como se no tivessem massa

    Partculas relativsticas sem massa

    Frmions de Dirac

    Neutrinos so Frmions de Dirac

    Neutrinos viajam a v=c, eltrons no grafeno tm v menor

    22

    22Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Como sabemos?

    23

    http://www.magnet.fsu.edu/education/tutorials/java/index.html

    Efeito Hall

    1879 Edwin H. Hall

    23Wednesday, January 19, 2011

    http://www.magnet.fsu.edu/education/tutorials/java/index.htmlhttp://www.magnet.fsu.edu/education/tutorials/java/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Efeito Hall

    24

    Eltrons em semicondutores e metais

    xy

    B(T)Inclinao da curva nos fornece nmero de eltrons/Volume

    Usado para caracterizar semicondutores

    24Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Efeito Hall quntico

    25

    T=-270oC

    xy=h/(e2N)

    N um nmero inteiro!

    h e e so constantes

    mas a baixa T e em 2D...

    25Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Efeito Hall quntico

    25

    T=-270oC

    xy=h/(e2N)

    N um nmero inteiro!

    h e e so constantes

    mas a baixa T e em 2D...

    12

    he2

    13

    he2

    25Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Efeito Hall quntico

    25

    Descoberto em 81 por Klaus von Klitzing, Nobel em 85

    Resistividade quantizada!

    Usado em metrologia como medida padro

    T=-270oC

    xy=h/(e2N)

    N um nmero inteiro!

    h e e so constantes

    Efeito Quntico!

    mas a baixa T e em 2D...

    12

    he2

    13

    he2

    25Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Efeito Hall quntico

    26

    Eltrons em semicondutores

    xy=h/(e2N)

    T=-270oC

    12

    he2

    13

    he2

    26Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Efeito Hall quntico

    26

    Eltrons em semicondutores

    xy=h/(e2N)

    16 Z. Jiang et al. / Solid State Communications 143 (2007) 1419

    Fig. 2. Quantized magnetoresistance and Hall resistance of a graphene devicewhere n 1012 cm2 and T = 1.6 K. The horizontal lines correspond to theinverse of the multiples e2/h. The QHE in the electron gas is demonstrated byat least two quantized plateaus in Rxy with vanishing Rxx in the correspondingmagnetic field regime.

    where the QHE manifests itself. Fig. 2 shows Rxy and Rxxof a typical high mobility ( > 10,000 cm2/V s) graphenesample as a function of magnetic field B at a fixed gatevoltage Vg > VDirac. The overall positive Rxy indicates that thecontribution is mainly from electrons. At high magnetic field,Rxy(B) exhibits plateaus and Rxx is vanishing, which are thehallmark of the QHE. At least two well-defined plateaus withvalues (2e2/h)1 and (6e2/h)1, followed by a developing(10e2/h)1 plateau, are observed before the QHE featurestransform into Shubnikovde Haas (SdH) oscillations at lowermagnetic field. We observed the equivalent QHE features forholes Vg < VDirac with negative Rxy(B) values.

    Alternatively we can access the QH plateaus by tuning theelectron density by adjusting Vg at a fixed magnetic field.Fig. 3 shows Rxy of the sample of Fig. 2 as a function ofgate voltage Vg at B = 9 T. A series of fully developed QHstates, i.e., plateaus in h/(e2) quantized to values with aninteger filling factor , are observed, which are the hallmarkof the QHE. Well-defined = 2, 6, 10, 14 QH statesare clearly seen, with quantization according to

    R1xy = 4(

    n + 12

    )e2

    h(1)

    where n is a non-negative integer, and +/ stands for electronsand holes respectively. This quantization condition can betranslated into the quantized filling factor = 4(n +1/2) in the usual QHE language. While the QHE has beenobserved in many 2D systems, the QHE observed in grapheneis distinctively different from those conventional QHEs sincethe quantization condition Eq. (1) is shifted by a half integer.

    This so-called half-integer QHE is unique to graphene.It has been predicted by several theories which combinerelativistic Landau levels (LLs) with the particlehole

    Fig. 3. The Hall resistance as a function of gate voltage at fixed magnetic fieldB = 9 T, measured at 1.6 K. The horizontal lines correspond to the inverse ofinteger multiples of e2/h values.

    symmetry of graphene [13]. The experimental phenomena canbe understood from the calculated LL spectrum in the Diracspectrum.

    As in other 2D systems, application of a magnetic field Bnormal to the graphene plane quantizes the in-plane motion ofcharge carriers into LLs. The LL formation for electrons/holesin graphene has been studied theoretically using an analogy to2 + 1 dimensional Quantum Electro Dynamics (QED) [4], inwhich the LL energy is given by

    En = sgn(n)

    2ehv2F |n|B. (2)Here e and h are electron charge and Plancks constant dividedby 2 , and the integer n represents an electron-like (n >0) or a hole-like (n < 0) LL index. In particular, a singleLL with n = 0 also occurs, where electrons and holes aredegenerate. Note that in Eq. (2). we do not consider a spindegree of freedom, assuming the separation of En is muchlarger than the Zeeman spin splitting. Therefore each LL hasa degeneracy gs = 4, accounting for spin degeneracy andsublattice degeneracy. This assumption needs to be changedwhen the magnetic field becomes large as we will discuss inthe next section.

    The observed QH sequence can be understood employingthe symmetry argument for the Hall conductivity xy =Rxy/(R2xy + (W/L)2 R2xx ), where L and W are the length andwidth of the sample, respectively. With the given LL spectrumin Eq. (2), the corresponding Hall conductance xy exhibitsQH plateaus when an integer of LLs are fully occupied, andjumps by an amount of gse2/h when the Fermi energy, EF ,crosses a LL. Time reversal invariance guarantees particleholesymmetry and thus xy is an odd function in energy acrossthe Dirac point [4]. Here, in particular, the n = 0 LL ispinned at zero energy. Thus the first plateau for electrons(n = 1) and holes (n = 1) are situated exactly at

    Eltrons no grafeno

    xy=h/(4e2(N+1/2))

    T=-270oC

    12

    he2

    13

    he2

    26Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Efeito Hall quntico

    26

    Eltrons em semicondutores

    xy=h/(e2N)

    16 Z. Jiang et al. / Solid State Communications 143 (2007) 1419

    Fig. 2. Quantized magnetoresistance and Hall resistance of a graphene devicewhere n 1012 cm2 and T = 1.6 K. The horizontal lines correspond to theinverse of the multiples e2/h. The QHE in the electron gas is demonstrated byat least two quantized plateaus in Rxy with vanishing Rxx in the correspondingmagnetic field regime.

    where the QHE manifests itself. Fig. 2 shows Rxy and Rxxof a typical high mobility ( > 10,000 cm2/V s) graphenesample as a function of magnetic field B at a fixed gatevoltage Vg > VDirac. The overall positive Rxy indicates that thecontribution is mainly from electrons. At high magnetic field,Rxy(B) exhibits plateaus and Rxx is vanishing, which are thehallmark of the QHE. At least two well-defined plateaus withvalues (2e2/h)1 and (6e2/h)1, followed by a developing(10e2/h)1 plateau, are observed before the QHE featurestransform into Shubnikovde Haas (SdH) oscillations at lowermagnetic field. We observed the equivalent QHE features forholes Vg < VDirac with negative Rxy(B) values.

    Alternatively we can access the QH plateaus by tuning theelectron density by adjusting Vg at a fixed magnetic field.Fig. 3 shows Rxy of the sample of Fig. 2 as a function ofgate voltage Vg at B = 9 T. A series of fully developed QHstates, i.e., plateaus in h/(e2) quantized to values with aninteger filling factor , are observed, which are the hallmarkof the QHE. Well-defined = 2, 6, 10, 14 QH statesare clearly seen, with quantization according to

    R1xy = 4(

    n + 12

    )e2

    h(1)

    where n is a non-negative integer, and +/ stands for electronsand holes respectively. This quantization condition can betranslated into the quantized filling factor = 4(n +1/2) in the usual QHE language. While the QHE has beenobserved in many 2D systems, the QHE observed in grapheneis distinctively different from those conventional QHEs sincethe quantization condition Eq. (1) is shifted by a half integer.

    This so-called half-integer QHE is unique to graphene.It has been predicted by several theories which combinerelativistic Landau levels (LLs) with the particlehole

    Fig. 3. The Hall resistance as a function of gate voltage at fixed magnetic fieldB = 9 T, measured at 1.6 K. The horizontal lines correspond to the inverse ofinteger multiples of e2/h values.

    symmetry of graphene [13]. The experimental phenomena canbe understood from the calculated LL spectrum in the Diracspectrum.

    As in other 2D systems, application of a magnetic field Bnormal to the graphene plane quantizes the in-plane motion ofcharge carriers into LLs. The LL formation for electrons/holesin graphene has been studied theoretically using an analogy to2 + 1 dimensional Quantum Electro Dynamics (QED) [4], inwhich the LL energy is given by

    En = sgn(n)

    2ehv2F |n|B. (2)Here e and h are electron charge and Plancks constant dividedby 2 , and the integer n represents an electron-like (n >0) or a hole-like (n < 0) LL index. In particular, a singleLL with n = 0 also occurs, where electrons and holes aredegenerate. Note that in Eq. (2). we do not consider a spindegree of freedom, assuming the separation of En is muchlarger than the Zeeman spin splitting. Therefore each LL hasa degeneracy gs = 4, accounting for spin degeneracy andsublattice degeneracy. This assumption needs to be changedwhen the magnetic field becomes large as we will discuss inthe next section.

    The observed QH sequence can be understood employingthe symmetry argument for the Hall conductivity xy =Rxy/(R2xy + (W/L)2 R2xx ), where L and W are the length andwidth of the sample, respectively. With the given LL spectrumin Eq. (2), the corresponding Hall conductance xy exhibitsQH plateaus when an integer of LLs are fully occupied, andjumps by an amount of gse2/h when the Fermi energy, EF ,crosses a LL. Time reversal invariance guarantees particleholesymmetry and thus xy is an odd function in energy acrossthe Dirac point [4]. Here, in particular, the n = 0 LL ispinned at zero energy. Thus the first plateau for electrons(n = 1) and holes (n = 1) are situated exactly at

    Eltrons no grafeno

    xy=h/(4e2(N+1/2))

    Partculas relativsticas sem massa

    T=-270oC

    Temperatura ambiente!

    12

    he2

    13

    he2

    12

    he2

    16

    he2

    110

    he2

    26Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Efeito Hall quntico no grafeno

    27

    16 Z. Jiang et al. / Solid State Communications 143 (2007) 1419

    Fig. 2. Quantized magnetoresistance and Hall resistance of a graphene devicewhere n 1012 cm2 and T = 1.6 K. The horizontal lines correspond to theinverse of the multiples e2/h. The QHE in the electron gas is demonstrated byat least two quantized plateaus in Rxy with vanishing Rxx in the correspondingmagnetic field regime.

    where the QHE manifests itself. Fig. 2 shows Rxy and Rxxof a typical high mobility ( > 10,000 cm2/V s) graphenesample as a function of magnetic field B at a fixed gatevoltage Vg > VDirac. The overall positive Rxy indicates that thecontribution is mainly from electrons. At high magnetic field,Rxy(B) exhibits plateaus and Rxx is vanishing, which are thehallmark of the QHE. At least two well-defined plateaus withvalues (2e2/h)1 and (6e2/h)1, followed by a developing(10e2/h)1 plateau, are observed before the QHE featurestransform into Shubnikovde Haas (SdH) oscillations at lowermagnetic field. We observed the equivalent QHE features forholes Vg < VDirac with negative Rxy(B) values.

    Alternatively we can access the QH plateaus by tuning theelectron density by adjusting Vg at a fixed magnetic field.Fig. 3 shows Rxy of the sample of Fig. 2 as a function ofgate voltage Vg at B = 9 T. A series of fully developed QHstates, i.e., plateaus in h/(e2) quantized to values with aninteger filling factor , are observed, which are the hallmarkof the QHE. Well-defined = 2, 6, 10, 14 QH statesare clearly seen, with quantization according to

    R1xy = 4(

    n + 12

    )e2

    h(1)

    where n is a non-negative integer, and +/ stands for electronsand holes respectively. This quantization condition can betranslated into the quantized filling factor = 4(n +1/2) in the usual QHE language. While the QHE has beenobserved in many 2D systems, the QHE observed in grapheneis distinctively different from those conventional QHEs sincethe quantization condition Eq. (1) is shifted by a half integer.

    This so-called half-integer QHE is unique to graphene.It has been predicted by several theories which combinerelativistic Landau levels (LLs) with the particlehole

    Fig. 3. The Hall resistance as a function of gate voltage at fixed magnetic fieldB = 9 T, measured at 1.6 K. The horizontal lines correspond to the inverse ofinteger multiples of e2/h values.

    symmetry of graphene [13]. The experimental phenomena canbe understood from the calculated LL spectrum in the Diracspectrum.

    As in other 2D systems, application of a magnetic field Bnormal to the graphene plane quantizes the in-plane motion ofcharge carriers into LLs. The LL formation for electrons/holesin graphene has been studied theoretically using an analogy to2 + 1 dimensional Quantum Electro Dynamics (QED) [4], inwhich the LL energy is given by

    En = sgn(n)

    2ehv2F |n|B. (2)Here e and h are electron charge and Plancks constant dividedby 2 , and the integer n represents an electron-like (n >0) or a hole-like (n < 0) LL index. In particular, a singleLL with n = 0 also occurs, where electrons and holes aredegenerate. Note that in Eq. (2). we do not consider a spindegree of freedom, assuming the separation of En is muchlarger than the Zeeman spin splitting. Therefore each LL hasa degeneracy gs = 4, accounting for spin degeneracy andsublattice degeneracy. This assumption needs to be changedwhen the magnetic field becomes large as we will discuss inthe next section.

    The observed QH sequence can be understood employingthe symmetry argument for the Hall conductivity xy =Rxy/(R2xy + (W/L)2 R2xx ), where L and W are the length andwidth of the sample, respectively. With the given LL spectrumin Eq. (2), the corresponding Hall conductance xy exhibitsQH plateaus when an integer of LLs are fully occupied, andjumps by an amount of gse2/h when the Fermi energy, EF ,crosses a LL. Time reversal invariance guarantees particleholesymmetry and thus xy is an odd function in energy acrossthe Dirac point [4]. Here, in particular, the n = 0 LL ispinned at zero energy. Thus the first plateau for electrons(n = 1) and holes (n = 1) are situated exactly at

    Partculas relativsticas sem massa

    Temperatura ambiente!

    Efeito Quntico!Einstein Bohr

    27Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport 28

    No aguento mais toda essa fsica! Que sono..

    Pra que serve esse tal de grafeno?

    28Wednesday, January 19, 2011

  • Outras propriedades

    29

    29Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    transparente

    30

    30Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    transparente

    30

    Imagem Y. P. Chen, Purdue University

    30Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    flexvel

    31

    Camada de grafeno depositada em polmero flexvel

    Imagem Rutgers

    31Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    flexvel

    31

    Camada de grafeno depositada em polmero flexvel

    Imagem SKKU KoreaImagem Rutgers

    31Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Pode ser dobrado e esticado

    32

    21

    32Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Pode ser dobrado e esticado

    32

    21

    Imagem Manchester

    32Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Grafeno

    33

    excelente condutor transparente ultra-resistente flexvel

    Para que serve?

    33Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Grafeno

    33

    E quais so as limitaes

    excelente condutor transparente ultra-resistente flexvel

    Para que serve?

    33Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Transistores na eletrnica

    Feitos de semicondutores

    Fundamentais em todos os circuitos eletrnicos

    34

    Amplificao

    Chaveamento (liga-desliga)

    Porta controla corrente entre entrada (fonte) e saida (dreno)

    F

    DP

    34Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    A vida antes do transistor

    35

    ENIAC 1946

    35Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    A vida antes do transistor

    35

    ENIAC 1946

    Bell Labs 1948Prmio Nobel de Fsica 1956Shockley, Bardeen, Brattain

    35Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Permitiu grande revoluo na eletrnica

    Circuitos desenhados em um nico semicondutor

    Circuitos integrados

    36

    36Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Permitiu grande revoluo na eletrnica

    Circuitos desenhados em um nico semicondutor

    Circuitos integrados

    36

    1958 Texas Instruments Prmio Nobel de Fsica 2000

    J. S. Kilby

    36Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Permitiu grande revoluo na eletrnica

    Circuitos desenhados em um nico semicondutor

    Circuitos integrados

    36

    1958 Texas Instruments Prmio Nobel de Fsica 2000

    J. S. Kilby

    36Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Fazendo um chip

    37

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.html

    37Wednesday, January 19, 2011

    http://nobelprize.org/educational/physics/integrated_circuit/history/index.htmlhttp://nobelprize.org/educational/physics/integrated_circuit/history/index.html

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport 38

    Mtodo do durex no pode ser usado em larga escalae produz folhas pequenas

    Novos mtodos de fabricao

    38Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport 38

    Mtodo do durex no pode ser usado em larga escalae produz folhas pequenas

    Novos mtodos de fabricao

    Deposio Qumica de Vapores (CVD)

    Epitaxia por feixe molecular

    Outros

    38Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport 38

    Mtodo do durex no pode ser usado em larga escalae produz folhas pequenas

    Novos mtodos de fabricao

    Deposio Qumica de Vapores (CVD)

    Epitaxia por feixe molecular

    Outros

    38Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Novos mtodos de fabricao

    39

    Co.) by applying soft pressure (!0.2 MPa) between two rollers.After etching the copper foil in a plastic bath filled with copperetchant, the transferred graphene film on the tape is rinsed withdeionized water to remove residual etchant, and is then ready tobe transferred to any kind of flat or curved surface on demand.The graphene film on the thermal release tape is inserted betweenthe rollers together with a target substrate and exposed tomild heat (!90120 8C), achieving a transfer rate of !150200 mm min21 and resulting in the transfer of the graphene films

    from the tape to the target substrate (Fig. 2b). By repeatingthese steps on the same substrate, multilayered graphene filmscan be prepared that exhibit enhanced electrical and opticalproperties, as demonstrated by Li and colleagues using wet-transfer methods at the centimetre scale19. Figure 2c shows the30-inch multilayer graphene film transferred to a roll of 188-mm-thick polyethylene terephthalate (PET) substrate. Figure 2d showsa screen-printing process used to fabricate four-wire touch-screenpanels18 based on graphene/PET transparent conducting films

    1st2nd30 inch

    Beforeheating

    Afterheating

    39 inch

    8 inch

    Stencil mask

    Screenprinter

    a d

    b e

    c f

    Figure 2 | Photographs of the roll-based production of graphene films. a, Copper foil wrapping around a 7.5-inch quartz tube to be inserted into an 8-inchquartz reactor. The lower image shows the stage in which the copper foil reacts with CH4 and H2 gases at high temperatures. b, Roll-to-roll transfer ofgraphene films from a thermal release tape to a PET film at 120 8C. c, A transparent ultralarge-area graphene film transferred on a 35-inch PET sheet.d, Screen printing process of silver paste electrodes on graphene/PET film. The inset shows 3.1-inch graphene/PET panels patterned with silver electrodesbefore assembly. e, An assembled graphene/PET touch panel showing outstanding flexibility. f, A graphene-based touch-screen panel connected to acomputer with control software. For a movie of its operation see Supplementary Information.

    Graphene on Cu foil

    Polymer support

    Cu etchant

    Graphene onpolymer support

    Target substrateGraphene on target

    Releasedpolymer support

    Figure 1 | Schematic of the roll-based production of graphene films grown on a copper foil.The process includes adhesion of polymer supports, copperetching (rinsing) and dry transfer-printing on a target substrate. A wet-chemical doping can be carried out using a set-up similar to that used for etching.

    LETTERS NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.132

    NATURE NANOTECHNOLOGY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturenanotechnology2

    Co.) by applying soft pressure (!0.2 MPa) between two rollers.After etching the copper foil in a plastic bath filled with copperetchant, the transferred graphene film on the tape is rinsed withdeionized water to remove residual etchant, and is then ready tobe transferred to any kind of flat or curved surface on demand.The graphene film on the thermal release tape is inserted betweenthe rollers together with a target substrate and exposed tomild heat (!90120 8C), achieving a transfer rate of !150200 mm min21 and resulting in the transfer of the graphene films

    from the tape to the target substrate (Fig. 2b). By repeatingthese steps on the same substrate, multilayered graphene filmscan be prepared that exhibit enhanced electrical and opticalproperties, as demonstrated by Li and colleagues using wet-transfer methods at the centimetre scale19. Figure 2c shows the30-inch multilayer graphene film transferred to a roll of 188-mm-thick polyethylene terephthalate (PET) substrate. Figure 2d showsa screen-printing process used to fabricate four-wire touch-screenpanels18 based on graphene/PET transparent conducting films

    1st2nd30 inch

    Beforeheating

    Afterheating

    39 inch

    8 inch

    Stencil mask

    Screenprinter

    a d

    b e

    c f

    Figure 2 | Photographs of the roll-based production of graphene films. a, Copper foil wrapping around a 7.5-inch quartz tube to be inserted into an 8-inchquartz reactor. The lower image shows the stage in which the copper foil reacts with CH4 and H2 gases at high temperatures. b, Roll-to-roll transfer ofgraphene films from a thermal release tape to a PET film at 120 8C. c, A transparent ultralarge-area graphene film transferred on a 35-inch PET sheet.d, Screen printing process of silver paste electrodes on graphene/PET film. The inset shows 3.1-inch graphene/PET panels patterned with silver electrodesbefore assembly. e, An assembled graphene/PET touch panel showing outstanding flexibility. f, A graphene-based touch-screen panel connected to acomputer with control software. For a movie of its operation see Supplementary Information.

    Graphene on Cu foil

    Polymer support

    Cu etchant

    Graphene onpolymer support

    Target substrateGraphene on target

    Releasedpolymer support

    Figure 1 | Schematic of the roll-based production of graphene films grown on a copper foil.The process includes adhesion of polymer supports, copperetching (rinsing) and dry transfer-printing on a target substrate. A wet-chemical doping can be carried out using a set-up similar to that used for etching.

    LETTERS NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.132

    NATURE NANOTECHNOLOGY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturenanotechnology2

    Junho de 2010

    Nature Nanotecnology 2010

    39Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Novos mtodos de fabricao

    39

    Co.) by applying soft pressure (!0.2 MPa) between two rollers.After etching the copper foil in a plastic bath filled with copperetchant, the transferred graphene film on the tape is rinsed withdeionized water to remove residual etchant, and is then ready tobe transferred to any kind of flat or curved surface on demand.The graphene film on the thermal release tape is inserted betweenthe rollers together with a target substrate and exposed tomild heat (!90120 8C), achieving a transfer rate of !150200 mm min21 and resulting in the transfer of the graphene films

    from the tape to the target substrate (Fig. 2b). By repeatingthese steps on the same substrate, multilayered graphene filmscan be prepared that exhibit enhanced electrical and opticalproperties, as demonstrated by Li and colleagues using wet-transfer methods at the centimetre scale19. Figure 2c shows the30-inch multilayer graphene film transferred to a roll of 188-mm-thick polyethylene terephthalate (PET) substrate. Figure 2d showsa screen-printing process used to fabricate four-wire touch-screenpanels18 based on graphene/PET transparent conducting films

    1st2nd30 inch

    Beforeheating

    Afterheating

    39 inch

    8 inch

    Stencil mask

    Screenprinter

    a d

    b e

    c f

    Figure 2 | Photographs of the roll-based production of graphene films. a, Copper foil wrapping around a 7.5-inch quartz tube to be inserted into an 8-inchquartz reactor. The lower image shows the stage in which the copper foil reacts with CH4 and H2 gases at high temperatures. b, Roll-to-roll transfer ofgraphene films from a thermal release tape to a PET film at 120 8C. c, A transparent ultralarge-area graphene film transferred on a 35-inch PET sheet.d, Screen printing process of silver paste electrodes on graphene/PET film. The inset shows 3.1-inch graphene/PET panels patterned with silver electrodesbefore assembly. e, An assembled graphene/PET touch panel showing outstanding flexibility. f, A graphene-based touch-screen panel connected to acomputer with control software. For a movie of its operation see Supplementary Information.

    Graphene on Cu foil

    Polymer support

    Cu etchant

    Graphene onpolymer support

    Target substrateGraphene on target

    Releasedpolymer support

    Figure 1 | Schematic of the roll-based production of graphene films grown on a copper foil.The process includes adhesion of polymer supports, copperetching (rinsing) and dry transfer-printing on a target substrate. A wet-chemical doping can be carried out using a set-up similar to that used for etching.

    LETTERS NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.132

    NATURE NANOTECHNOLOGY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturenanotechnology2

    Co.) by applying soft pressure (!0.2 MPa) between two rollers.After etching the copper foil in a plastic bath filled with copperetchant, the transferred graphene film on the tape is rinsed withdeionized water to remove residual etchant, and is then ready tobe transferred to any kind of flat or curved surface on demand.The graphene film on the thermal release tape is inserted betweenthe rollers together with a target substrate and exposed tomild heat (!90120 8C), achieving a transfer rate of !150200 mm min21 and resulting in the transfer of the graphene films

    from the tape to the target substrate (Fig. 2b). By repeatingthese steps on the same substrate, multilayered graphene filmscan be prepared that exhibit enhanced electrical and opticalproperties, as demonstrated by Li and colleagues using wet-transfer methods at the centimetre scale19. Figure 2c shows the30-inch multilayer graphene film transferred to a roll of 188-mm-thick polyethylene terephthalate (PET) substrate. Figure 2d showsa screen-printing process used to fabricate four-wire touch-screenpanels18 based on graphene/PET transparent conducting films

    1st2nd30 inch

    Beforeheating

    Afterheating

    39 inch

    8 inch

    Stencil mask

    Screenprinter

    a d

    b e

    c f

    Figure 2 | Photographs of the roll-based production of graphene films. a, Copper foil wrapping around a 7.5-inch quartz tube to be inserted into an 8-inchquartz reactor. The lower image shows the stage in which the copper foil reacts with CH4 and H2 gases at high temperatures. b, Roll-to-roll transfer ofgraphene films from a thermal release tape to a PET film at 120 8C. c, A transparent ultralarge-area graphene film transferred on a 35-inch PET sheet.d, Screen printing process of silver paste electrodes on graphene/PET film. The inset shows 3.1-inch graphene/PET panels patterned with silver electrodesbefore assembly. e, An assembled graphene/PET touch panel showing outstanding flexibility. f, A graphene-based touch-screen panel connected to acomputer with control software. For a movie of its operation see Supplementary Information.

    Graphene on Cu foil

    Polymer support

    Cu etchant

    Graphene onpolymer support

    Target substrateGraphene on target

    Releasedpolymer support

    Figure 1 | Schematic of the roll-based production of graphene films grown on a copper foil.The process includes adhesion of polymer supports, copperetching (rinsing) and dry transfer-printing on a target substrate. A wet-chemical doping can be carried out using a set-up similar to that used for etching.

    LETTERS NATURE NANOTECHNOLOGY DOI: 10.1038/NNANO.2010.132

    NATURE NANOTECHNOLOGY | ADVANCE ONLINE PUBLICATION | www.nature.com/naturenanotechnology2

    SiO2 (300 nm)

    Ni/C layer

    CH4/H2/Ar

    ~1,000 C

    Ar

    Cooling~RT

    Patterned Ni layer (300 nm)

    FeCl3(aq)or acids

    Ni-layeretching

    HF/BOE

    SiO2-layeretching(short)

    Ni-layeretching(long)

    PDMS/graphene

    Downside contact(scooping up)

    Graphene on a substrate

    HF/BOE

    Stamping

    Floating graphene/Ni Floating grapheneGraphene/Ni/SiO2/Si

    a

    b

    c

    PDMS/graphene/Ni/SiO2/Si

    NiSi

    Figure 1 | Synthesis, etching andtransfer processes for the large-scale and patterned graphenefilms. a, Synthesis of patternedgraphene films on thin nickel layers.b, Etching using FeCl3 (or acids)and transfer of graphene films usinga PDMS stamp. c, Etching usingBOE or hydrogen fluoride (HF)solution and transfer of graphenefilms. RT, room temperature(,25 uC).

    1,500 2,000 2,500

    Inte

    nsity

    (a.u

    .)

    Raman shift (cm1)

    >4 layers3 layersBilayerMonolayer

    a

    c

    5 m

    5 m

    e

    5 m

    = 532 nm

    2 m

    3 layers

    Bilayer45 layers

    0.34 nm

    b

    >10 layers

    G

    2DD

    5 m

    d >54321

    Figure 2 | Various spectroscopic analyses of the large-scale graphene filmsgrownby CVD. a, SEM images of as-grown graphene films on thin (300-nm)nickel layers and thick (1-mm) Ni foils (inset). b, TEM images of graphenefilms of different thicknesses. c, An optical microscope image of thegraphene film transferred to a 300-nm-thick silicon dioxide layer. The insetAFM image shows typical rippled structures. d, A confocal scanning Ramanimage corresponding to c. The number of layers is estimated from theintensities, shapes andpositions of theG-band and 2D-bandpeaks. e, Ramanspectra (532-nm laser wavelength) obtained from the correspondingcoloured spots in c and d. a.u., arbitrary units.

    d e

    g h

    2 cm

    2 cm

    Stamping Patterned graphene

    a b

    f

    c

    5 mm

    Figure 3 | Transfer processes for large-scale graphene films. a, Acentimetre-scale graphene film grown on a Ni(300 nm)/SiO2(300 nm)/Sisubstrate. b, A floating graphene film after etching the nickel layers in 1MFeCl3 aqueous solution. After the removal of the nickel layers, the floatinggraphene film can be transferred by direct contact with substrates. c, Variousshapes of graphene films can be synthesized on top of patternednickel layers.d, e, The dry-transfer method based on a PDMS stamp is useful intransferring the patterned graphene films. After attaching the PDMSsubstrate to the graphene (d), the underlying nickel layer is etched andremoved using FeCl3 solution (e). f, Graphene films on the PDMS substratesare transparent and flexible. g, h, The PDMS stampmakes conformal contactwith a silicon dioxide substrate. Peeling back the stamp (g) leaves the film ona SiO2 substrate (h).

    NATURE |Vol 457 |5 February 2009 LETTERS

    707 Macmillan Publishers Limited. All rights reserved2009

    Mas....Junho de 2010

    Nature Nanotecnology 2010

    39Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Circuitos integrados

    40

    SiO2 (300 nm)

    Ni/C layer

    CH4/H2/Ar

    ~1,000 C

    Ar

    Cooling~RT

    Patterned Ni layer (300 nm)

    FeCl3(aq)or acids

    Ni-layeretching

    HF/BOE

    SiO2-layeretching(short)

    Ni-layeretching(long)

    PDMS/graphene

    Downside contact(scooping up)

    Graphene on a substrate

    HF/BOE

    Stamping

    Floating graphene/Ni Floating grapheneGraphene/Ni/SiO2/Si

    a

    b

    c

    PDMS/graphene/Ni/SiO2/Si

    NiSi

    Figure 1 | Synthesis, etching andtransfer processes for the large-scale and patterned graphenefilms. a, Synthesis of patternedgraphene films on thin nickel layers.b, Etching using FeCl3 (or acids)and transfer of graphene films usinga PDMS stamp. c, Etching usingBOE or hydrogen fluoride (HF)solution and transfer of graphenefilms. RT, room temperature(,25 uC).

    1,500 2,000 2,500

    Inte

    nsity

    (a.u

    .)

    Raman shift (cm1)

    >4 layers3 layersBilayerMonolayer

    a

    c

    5 m

    5 m

    e

    5 m

    = 532 nm

    2 m

    3 layers

    Bilayer45 layers

    0.34 nm

    b

    >10 layers

    G

    2DD

    5 m

    d >54321

    Figure 2 | Various spectroscopic analyses of the large-scale graphene filmsgrownby CVD. a, SEM images of as-grown graphene films on thin (300-nm)nickel layers and thick (1-mm) Ni foils (inset). b, TEM images of graphenefilms of different thicknesses. c, An optical microscope image of thegraphene film transferred to a 300-nm-thick silicon dioxide layer. The insetAFM image shows typical rippled structures. d, A confocal scanning Ramanimage corresponding to c. The number of layers is estimated from theintensities, shapes andpositions of theG-band and 2D-bandpeaks. e, Ramanspectra (532-nm laser wavelength) obtained from the correspondingcoloured spots in c and d. a.u., arbitrary units.

    d e

    g h

    2 cm

    2 cm

    Stamping Patterned graphene

    a b

    f

    c

    5 mm

    Figure 3 | Transfer processes for large-scale graphene films. a, Acentimetre-scale graphene film grown on a Ni(300 nm)/SiO2(300 nm)/Sisubstrate. b, A floating graphene film after etching the nickel layers in 1MFeCl3 aqueous solution. After the removal of the nickel layers, the floatinggraphene film can be transferred by direct contact with substrates. c, Variousshapes of graphene films can be synthesized on top of patternednickel layers.d, e, The dry-transfer method based on a PDMS stamp is useful intransferring the patterned graphene films. After attaching the PDMSsubstrate to the graphene (d), the underlying nickel layer is etched andremoved using FeCl3 solution (e). f, Graphene films on the PDMS substratesare transparent and flexible. g, h, The PDMS stampmakes conformal contactwith a silicon dioxide substrate. Peeling back the stamp (g) leaves the film ona SiO2 substrate (h).

    NATURE |Vol 457 |5 February 2009 LETTERS

    707 Macmillan Publishers Limited. All rights reserved2009

    SKKY/ Columbia U.,Nature 2009

    40Wednesday, January 19, 2011

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    Novos mtodos de fabricao

    Mtodos novos ainda no produzem folhas de grafeno homogneas

    Importante para mobilidade alta transistores

    No to importante para outras aplicaes

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    excelente condutor transparente ultra-resistente flexvel

    41Wednesday, January 19, 2011

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    42Wednesday, January 19, 2011

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    Aplicaes

    Atualmente xido de ndio dopado com Estanho (ITO)

    ndio raro, caro e difcil de reciclar

    Substituio ir baratear produo

    Produo ser mais limpa

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    Filme transparente e condutor para LCD, touch screen, clulas solares e qualquer coisa que precise de um contato transparente

    42Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Aplicaes

    Atualmente xido de ndio dopado com Estanho (ITO)

    ndio raro, caro e difcil de reciclar

    Substituio ir baratear produo

    Produo ser mais limpa

    42

    Filme transparente e condutor para LCD, touch screen, clulas solares e qualquer coisa que precise de um contato transparente

    Produo em larga escala para substituio do ITO nos prximos anos

    42Wednesday, January 19, 2011

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    Touch Screen de grafenoProttipo da Samsung, junto com pesquisadores da SKKU

    43

    43Wednesday, January 19, 2011

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    Touch Screen de grafenoProttipo da Samsung, junto com pesquisadores da SKKU

    43

    43Wednesday, January 19, 2011

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    Transistores de grafeno

    44

    Fevereiro de 2010

    44Wednesday, January 19, 2011

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    Transistores de grafeno

    Prottipos operam a 100-200 GHz

    Devem chegar facilmente a 1THz

    Tamanho de alguns nm

    44

    Fevereiro de 2010

    44Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Transistores de grafeno

    Prottipos operam a 100-200 GHz

    Devem chegar facilmente a 1THz

    Tamanho de alguns nm

    Transistores para eletrnica analgica

    Substituio de transistores de GaAs

    para RF uso militar, comunicaes

    44

    Fevereiro de 2010

    44Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Transistores de grafeno

    Prottipos operam a 100-200 GHz

    Devem chegar facilmente a 1THz

    Tamanho de alguns nm

    Transistores para eletrnica analgica

    Substituio de transistores de GaAs

    para RF uso militar, comunicaes

    44

    Fevereiro de 2010

    Produo nos prximos 5 anos

    44Wednesday, January 19, 2011

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    Transistores de um nico eltron

    45

    F

    DP

    F DP

    45Wednesday, January 19, 2011

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    Transistores de um nico eltron

    45

    F

    DP

    F DP

    Manchester 2008

    P

    F D

    45Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Transistores de um nico eltron

    45

    degeneracy at large n and l, and the number ofstates around a given energy is proportional to thedot area D2. This effect is often referred to asthe level repulsion, a universal signature of quan-tum chaos. The observed random spacing of CBpeaks, random height of Coulomb diamonds,changes in DVg quicker than 1/D and, especial-ly, the pronounced broadening of the spectraldistribution all indicate that chaos becomes adominant factor for small QDs.

    To corroborate this further, Fig. 3 shows that theobserved level spacing is well described by Gauss-ian unitary distribution (32/p2)dE2exp(4dE2/p)(characteristic of chaotic billiards) rather than thePoisson statistics exp(dE) expected for integra-ble geometries (25, 26). The CB energy shifts thestatistical distributions from zero (we measureDE =Ec + dE rather than dE), and this makes itdifficult to distinguish between unitary and or-thogonal ensembles. Nevertheless, the Gaussianunitary distribution fits our data notably better.This agrees with the theory that expects randomedges to break down the sublattice symmetry(27) leading to the unitary statistics (25). In termsof statistics, Dirac billiards are different from thechaotic wave systems that mimic quantum me-chanics and are also described by the linear dis-

    persion relation (optical, microwave, and acousticcavities) but typically obey the Gaussian orthog-onal statistics (28). Further evidence for the levelrepulsion in small QDs is provided by the ab-sence of any apparent bunching in their spectra(Fig. 2C). Indeed, despite considerable effort, wedid not find repetitive quartets or pairs of CBpeaks, which in principle could be expected dueto spin and/or valley degeneracy. The latter de-generacy is lifted by edge scattering (27), whereasthe spin degeneracy may be removed by scat-tering on localized spins due to broken carbonbonds (5).

    For even smaller devices (D < 30nm), theexperimental behavior is completely dominated byquantum confinement. They exhibit insulatingregions in Vg sometimes as large as several V,and their stability diagrams yield the level spacingexceeding ~50 meV (Fig. 4, A and B). However,because even the state-of-the-art lithography doesnot allow one to control features 30 V) (off state),but then it suddenly switches on, exhibitingrather high G 103e2/h. At large biases, weobserve the conductance onset shifting with Vb(13), which allows an estimate forDE as 0.5 eV.This value agrees with the T dependencemeasured near the onset of the on state, whichshows that we do not deal with several QDs inseries [as it was argued to be the case fornanoribbons (29)]. With no possibility to controlthe exact geometry for the nm sizes, we cannot becertain about the origin of the observed switching.Also, the exact boundary arrangements (armchairversus zigzag versus random edge and the ter-mination of dangling bonds) can be important onthis scale (512). Nevertheless,dE ~ 0.5 eVagainallows us to estimate the spatial scale involved inthe confinement as only ~1 nm.

    Our work demonstrates that graphene QDsare an interesting and versatile experimental

    system allowing a range of operational regimesfrom conventional single-electron detectors toDirac billiards, in which size effects are excep-tionally strong and chaos develops easily. Unlikeany other material, graphene remains mechani-cally and chemically stable and highly conduc-tive at the scale of a few benzene rings, whichmakes it uniquely suitable for the top-downapproach to molecular-scale electronics.

    References and Notes1. A. K. Geim, K. S. Novoselov, Nat. Mater. 6, 183 (2007).2. A. H. Castro Neto, F. Guinea, N. M. R. Peres,

    K. S. Novoselov, A. K. Geim, Rev. Mod. Phys., in press;preprint at http://xxx.lanl.gov/abs/0709.1163 (2007).

    3. M. Y. Han, B. Ozyilmaz, Y. B. Zhang, P. Kim, Phys. Rev.Lett. 98, 206805 (2007).

    4. P. Avouris, Z. H. Chen, V. Perebeinos, Nat. Nanotechnol.2, 605 (2007).

    5. Y. W. Son, M. L. Cohen, S. G. Louie,Nature 444, 347 (2006).6. D. Gunlycke, D. A. Areshkin, C. T. White, Appl. Phys. Lett.

    90, 142104 (2007).7. L. Yang, C. H. Park, Y. W. Son, M. L. Cohen, S. G. Louie,

    Phys. Rev. Lett. 99, 186801 (2007).8. N. M. R. Peres, A. H. Castro Neto, F. Guinea, Phys. Rev. B

    73, 195411 (2006).9. V. Barone, O. Hod, G. E. Scuseria,Nano Lett. 6, 2748 (2006).

    10. L. Brey, H. A. Fertig, Phys. Rev. B 73, 235411 (2006).11. B. Wunsch, T. Stauber, F. Guinea, Phys. Rev. B 77,

    035316 (2008).12. I. Martin, Y. M. Blanter, preprint at http://lanl.arxiv.org/

    abs/0705.0532 (2007).13. See supporting material on Science Online.14. K. K. Likharev, Proc. IEEE 87, 606 (1999).15. L. P. Kouwenhoven et al., in Mesoscopic Electron

    Transport, L. L. Sohn, L. P. Kouwenhoven, G. Schn,Eds. (Kluwer Series E345, Dordrecht, Netherlands, 1997),pp. 105214.

    16. E. A. Dobisz, S. L. Brandow, R. Bass, J. Mitterender, J. Vac.Sci. Technol. B 18, 107 (2000).

    17. B. Gelmont, M. S. Shur, R. J. Mattauch, Solid StateElectron. 38, 731 (1995).

    18. J. S. Bunch, Y. Yaish, M. Brink, K. Bolotin, P. L. McEuen,Nano Lett. 5, 287 (2005).

    19. F. Miao et al., Science 317, 1530 (2007).20. C. Stampfer et al., Appl. Phys. Lett. 92, 012102 (2008).21. U. Sivan et al., Phys. Rev. Lett. 77, 1123 (1996).22. S. R. Patel et al., Phys. Rev. Lett. 80, 4522 (1998).23. P. G. Silvestrov, K. B. Efetov, Phys. Rev. Lett. 98, 016802

    (2007).24. I. M. Ruzin, V. Chandrasekhar, E. I. Levin, L. I. Glazman,

    Phys. Rev. B 45, 13469 (1992).25. M. V. Berry, R. J. Mondragon, Proc. R. Soc. London A

    412, 53 (1987).26. T. Guhr, A. Mller-Groeling, H. A. Weinedmller, Phys.

    Rep. 299, 189 (1998).27. A. Rycerz, J. Tworzydlo, C. W. J. Beenakker, Nat. Phys 3,

    172 (2007).28. U. Kuhl, H.-J. Stckmann, R. Weaver, J. Phys. A 38,

    10433 (2005).29. F. Sols, F. Guinea, A. H. Castro Neto, Phys. Rev. Lett. 99,

    166803 (2007).30. The research was supported by Engineering and Physical

    Sciences Research Council (UK), the Royal Society, andOffice of Naval Research. We are grateful to K. Ensslin,L. Eaves, M. Berry, L. Vandersypen, A. Morpurgo,A. Castro Neto, F. Guinea, and M. Fromhold for helpfuldiscussions.

    Supporting Online Materialwww.sciencemag.org/cgi/content/full/320/5874/356/DC1Materials and MethodsSOM TextFigs. S1 to S5References

    27 December 2007; accepted 5 March 200810.1126/science.1154663

    A

    B

    C( (

    (

    )

    Fig. 4. Electron transport through nm-scalegraphene devices. CB peaks (A) and diamonds (B)for a QDwith an estimated size ~ 15 nm. (C) Electrontransport through a controllably narrowed devicewith a minimal width of only 1 nm as estimatedfrom its DE. Its conductance can be completelypinched-off even at room T. Fluctuations in the onstate at room T are time dependent (excess noise). Atlow T, the on state exhibits much lower G, and thenoise disappears. Occasional transmission resonancescan also be seen as magnified in the inset.

    18 APRIL 2008 VOL 320 SCIENCE www.sciencemag.org358

    REPORTS

    on A

    pril 1

    7, 20

    08

    w

    ww

    .scie

    nce

    ma

    g.o

    rgD

    ow

    nlo

    ad

    ed

    fro

    m

    ~1 nm

    F

    DP

    F DP

    Manchester 2008

    P

    F D

    45Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Transistores de um nico eltron

    45

    degeneracy at large n and l, and the number ofstates around a given energy is proportional to thedot area D2. This effect is often referred to asthe level repulsion, a universal signature of quan-tum chaos. The observed random spacing of CBpeaks, random height of Coulomb diamonds,changes in DVg quicker than 1/D and, especial-ly, the pronounced broadening of the spectraldistribution all indicate that chaos becomes adominant factor for small QDs.

    To corroborate this further, Fig. 3 shows that theobserved level spacing is well described by Gauss-ian unitary distribution (32/p2)dE2exp(4dE2/p)(characteristic of chaotic billiards) rather than thePoisson statistics exp(dE) expected for integra-ble geometries (25, 26). The CB energy shifts thestatistical distributions from zero (we measureDE =Ec + dE rather than dE), and this makes itdifficult to distinguish between unitary and or-thogonal ensembles. Nevertheless, the Gaussianunitary distribution fits our data notably better.This agrees with the theory that expects randomedges to break down the sublattice symmetry(27) leading to the unitary statistics (25). In termsof statistics, Dirac billiards are different from thechaotic wave systems that mimic quantum me-chanics and are also described by the linear dis-

    persion relation (optical, microwave, and acousticcavities) but typically obey the Gaussian orthog-onal statistics (28). Further evidence for the levelrepulsion in small QDs is provided by the ab-sence of any apparent bunching in their spectra(Fig. 2C). Indeed, despite considerable effort, wedid not find repetitive quartets or pairs of CBpeaks, which in principle could be expected dueto spin and/or valley degeneracy. The latter de-generacy is lifted by edge scattering (27), whereasthe spin degeneracy may be removed by scat-tering on localized spins due to broken carbonbonds (5).

    For even smaller devices (D < 30nm), theexperimental behavior is completely dominated byquantum confinement. They exhibit insulatingregions in Vg sometimes as large as several V,and their stability diagrams yield the level spacingexceeding ~50 meV (Fig. 4, A and B). However,because even the state-of-the-art lithography doesnot allow one to control features 30 V) (off state),but then it suddenly switches on, exhibitingrather high G 103e2/h. At large biases, weobserve the conductance onset shifting with Vb(13), which allows an estimate forDE as 0.5 eV.This value agrees with the T dependencemeasured near the onset of the on state, whichshows that we do not deal with several QDs inseries [as it was argued to be the case fornanoribbons (29)]. With no possibility to controlthe exact geometry for the nm sizes, we cannot becertain about the origin of the observed switching.Also, the exact boundary arrangements (armchairversus zigzag versus random edge and the ter-mination of dangling bonds) can be important onthis scale (512). Nevertheless,dE ~ 0.5 eVagainallows us to estimate the spatial scale involved inthe confinement as only ~1 nm.

    Our work demonstrates that graphene QDsare an interesting and versatile experimental

    system allowing a range of operational regimesfrom conventional single-electron detectors toDirac billiards, in which size effects are excep-tionally strong and chaos develops easily. Unlikeany other material, graphene remains mechani-cally and chemically stable and highly conduc-tive at the scale of a few benzene rings, whichmakes it uniquely suitable for the top-downapproach to molecular-scale electronics.

    References and Notes1. A. K. Geim, K. S. Novoselov, Nat. Mater. 6, 183 (2007).2. A. H. Castro Neto, F. Guinea, N. M. R. Peres,

    K. S. Novoselov, A. K. Geim, Rev. Mod. Phys., in press;preprint at http://xxx.lanl.gov/abs/0709.1163 (2007).

    3. M. Y. Han, B. Ozyilmaz, Y. B. Zhang, P. Kim, Phys. Rev.Lett. 98, 206805 (2007).

    4. P. Avouris, Z. H. Chen, V. Perebeinos, Nat. Nanotechnol.2, 605 (2007).

    5. Y. W. Son, M. L. Cohen, S. G. Louie,Nature 444, 347 (2006).6. D. Gunlycke, D. A. Areshkin, C. T. White, Appl. Phys. Lett.

    90, 142104 (2007).7. L. Yang, C. H. Park, Y. W. Son, M. L. Cohen, S. G. Louie,

    Phys. Rev. Lett. 99, 186801 (2007).8. N. M. R. Peres, A. H. Castro Neto, F. Guinea, Phys. Rev. B

    73, 195411 (2006).9. V. Barone, O. Hod, G. E. Scuseria,Nano Lett. 6, 2748 (2006).

    10. L. Brey, H. A. Fertig, Phys. Rev. B 73, 235411 (2006).11. B. Wunsch, T. Stauber, F. Guinea, Phys. Rev. B 77,

    035316 (2008).12. I. Martin, Y. M. Blanter, preprint at http://lanl.arxiv.org/

    abs/0705.0532 (2007).13. See supporting material on Science Online.14. K. K. Likharev, Proc. IEEE 87, 606 (1999).15. L. P. Kouwenhoven et al., in Mesoscopic Electron

    Transport, L. L. Sohn, L. P. Kouwenhoven, G. Schn,Eds. (Kluwer Series E345, Dordrecht, Netherlands, 1997),pp. 105214.

    16. E. A. Dobisz, S. L. Brandow, R. Bass, J. Mitterender, J. Vac.Sci. Technol. B 18, 107 (2000).

    17. B. Gelmont, M. S. Shur, R. J. Mattauch, Solid StateElectron. 38, 731 (1995).

    18. J. S. Bunch, Y. Yaish, M. Brink, K. Bolotin, P. L. McEuen,Nano Lett. 5, 287 (2005).

    19. F. Miao et al., Science 317, 1530 (2007).20. C. Stampfer et al., Appl. Phys. Lett. 92, 012102 (2008).21. U. Sivan et al., Phys. Rev. Lett. 77, 1123 (1996).22. S. R. Patel et al., Phys. Rev. Lett. 80, 4522 (1998).23. P. G. Silvestrov, K. B. Efetov, Phys. Rev. Lett. 98, 016802

    (2007).24. I. M. Ruzin, V. Chandrasekhar, E. I. Levin, L. I. Glazman,

    Phys. Rev. B 45, 13469 (1992).25. M. V. Berry, R. J. Mondragon, Proc. R. Soc. London A

    412, 53 (1987).26. T. Guhr, A. Mller-Groeling, H. A. Weinedmller, Phys.

    Rep. 299, 189 (1998).27. A. Rycerz, J. Tworzydlo, C. W. J. Beenakker, Nat. Phys 3,

    172 (2007).28. U. Kuhl, H.-J. Stckmann, R. Weaver, J. Phys. A 38,

    10433 (2005).29. F. Sols, F. Guinea, A. H. Castro Neto, Phys. Rev. Lett. 99,

    166803 (2007).30. The research was supported by Engineering and Physical

    Sciences Research Council (UK), the Royal Society, andOffice of Naval Research. We are grateful to K. Ensslin,L. Eaves, M. Berry, L. Vandersypen, A. Morpurgo,A. Castro Neto, F. Guinea, and M. Fromhold for helpfuldiscussions.

    Supporting Online Materialwww.sciencemag.org/cgi/content/full/320/5874/356/DC1Materials and MethodsSOM TextFigs. S1 to S5References

    27 December 2007; accepted 5 March 200810.1126/science.1154663

    A

    B

    C( (

    (

    )

    Fig. 4. Electron transport through nm-scalegraphene devices. CB peaks (A) and diamonds (B)for a QDwith an estimated size ~ 15 nm. (C) Electrontransport through a controllably narrowed devicewith a minimal width of only 1 nm as estimatedfrom its DE. Its conductance can be completelypinched-off even at room T. Fluctuations in the onstate at room T are time dependent (excess noise). Atlow T, the on state exhibits much lower G, and thenoise disappears. Occasional transmission resonancescan also be seen as magnified in the inset.

    18 APRIL 2008 VOL 320 SCIENCE www.sciencemag.org358

    REPORTS

    on A

    pril 1

    7, 20

    08

    w

    ww

    .scie

    nce

    ma

    g.o

    rgD

    ow

    nlo

    ad

    ed

    fro

    m

    ~1 nm

    F

    DP

    F DP

    Manchester 2008

    P

    F DAinda muito trabalho pela frente para produo em grande escala!

    45Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

    Outras aplicaes

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    46Wednesday, January 19, 2011

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    46

    Sensores de gs

    46Wednesday, January 19, 2011

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    IBM

    Fotodetectores

    Sensores de gs

    46Wednesday, January 19, 2011

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    IBM

    Fotodetectores

    Fluorografeno(teflon)

    Sensores de gs

    46Wednesday, January 19, 2011

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    IBM

    Fotodetectores

    Fluorografeno(teflon)

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    Ultracapacitores

    46Wednesday, January 19, 2011

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    IBM

    Fotodetectores

    Fluorografeno(teflon)

    Sensores de gs

    Strain Engineering of Graphenes Electronic Structure

    Vitor M. Pereira and A.H. Castro NetoDepartment of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA

    (Received 13 February 2009; published 20 July 2009)

    We explore the influence of local strain on the electronic structure of graphene. We show that strain can

    be easily tailored to generate electron beam collimation, 1D channels, surface states, and confinement.

    These can be seen as basic elements for all-graphene electronics which, by suitable engineering of local

    strain profiles, could be integrated on a single graphene sheet. In addition this proposal has the advantage

    that patterning can be made on substrates rather than on graphene, thereby protecting the integrity of the

    latter.

    DOI: 10.1103/PhysRevLett.103.046801 PACS numbers: 81.05.Uw, 73.90.+f, 85.30.Mn

    Notwithstanding its atomic thickness, graphene sheetshave been shown to accommodate a wealth of remarkablefundamental properties, and to hold sound prospects in thecontext of a new generation of electronic devices andcircuitry [1]. One exciting prospect about graphene isthat, not only can we have extremely good conductors,but also most active devices made out of graphene. Currentdifficulties with respect to this goal lie in that conventionalelectronic operations require the ability to completelypinch off the charge transport on demand. Although theelectric field effect is impressive in graphene [2], the ex-istence of a minimum of conductivity poses a seriousobstacle towards desirable on/off ratios. A gapped spec-trum would certainly be instrumental. The presence of agap is implicitly related to the problem of electron con-finement, which for Dirac fermions is not easily achievableby conventional means (like electrostatic potential wells)[3]. Geometrical confinement has been achieved in gra-phene ribbons and dots [4,5], but the sensitivity of transportto the edge profile [6], and the inherent difficulty in thefabrication of such microstructures with sharply definededges remains a problem.

    The ultimate goal would be an all-graphene circuit. Thiscould be achieved by taking a graphene sheet and pattern-ing the different devices and leads by means of appropriatecuts that would generate leads, ribbons, dots, etc. Thispaper cutting electronics can have serious limitationswith respect to reliability, scalability, and is prone todamaging and inducing disorder in the graphene sheet[7]. Therefore, in keeping with the paper art analogy, wepropose an alternative origami electronics [8].

    We show here that all of the characteristics of grapheneribbons and dots (viz. geometrical quantization, 1D chan-nels, surface modes) might be locally obtained by pattern-ing, not graphene, but the substrate on which it rests. Theessential aspect of our approach is the generation of strainin the graphene lattice capable of changing the in-planehopping amplitude in an anisotropic way. This can beachieved by means of appropriate geometrical patterns ina homogeneous substrate (grooves, creases, steps, orwells), by means of a heterogeneous substrate in which

    different regions interact differently with the graphenesheet, generating different strain profiles [Fig. 1(b)].Another design alternative consists in depositing grapheneonto substrates with regions that can be controllablystrained on demand [9], or by exploring substrates withthermal expansion heterogeneity. Through a combinationof folding and/or clamping a graphene sheet onto suchsubstrates, one might generate local strain profiles suitablefor the applications discussed in detail below, while pre-serving a whole graphene sheet.The remainder of the Letter is dedicated to showing how

    strain only can be used as a means of achieving (i) directiondependent tunneling, (ii) beam collimation, (iii) con-finement, (iv) the spectrum of an effective ribbon, (v) 1Dchannels, and (vi) surface modes.Model.Within a tight-binding formulation of the elec-

    tronic motion [10], effects of in-plane strain can be cap-tured, to leading order, by considering the changes innearest-neighbor hopping amplitude, t. We writetRi;n t !tRi;n, and treat the space dependentstrain-induced modulation, !t, as a perturbation (t %3 eV). It is straightforward to show [10] that, for smoothperturbations, the low energy Hamiltonian is

    H vFZ

    dr!y! &

    !p' 1vFA

    "0

    0 '! &!p 1vF A

    "24

    35!;

    (1)

    valid near the valleys K and K0 in the Brillouin zone, with

    FIG. 1 (color online). (a) Lattice orientation considered in thetext. Thicker bonds have perturbed hopping. (b) Artistic depic-tion of a substrate (S) patterned with folds (F), trenches, dots andwells (A), upon which rests a graphene sheet (G).

    PRL 103, 046801 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending24 JULY 2009

    0031-9007=09=103(4)=046801(4) 046801-1 ! 2009 The American Physical Society

    Eletrnica origami

    Ultracapacitores

    46Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

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    46

    IBM

    Fotodetectores

    xido de grafeno

    Fluorografeno(teflon)

    Sensores de gs

    Strain Engineering of Graphenes Electronic Structure

    Vitor M. Pereira and A.H. Castro NetoDepartment of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA

    (Received 13 February 2009; published 20 July 2009)

    We explore the influence of local strain on the electronic structure of graphene. We show that strain can

    be easily tailored to generate electron beam collimation, 1D channels, surface states, and confinement.

    These can be seen as basic elements for all-graphene electronics which, by suitable engineering of local

    strain profiles, could be integrated on a single graphene sheet. In addition this proposal has the advantage

    that patterning can be made on substrates rather than on graphene, thereby protecting the integrity of the

    latter.

    DOI: 10.1103/PhysRevLett.103.046801 PACS numbers: 81.05.Uw, 73.90.+f, 85.30.Mn

    Notwithstanding its atomic thickness, graphene sheetshave been shown to accommodate a wealth of remarkablefundamental properties, and to hold sound prospects in thecontext of a new generation of electronic devices andcircuitry [1]. One exciting prospect about graphene isthat, not only can we have extremely good conductors,but also most active devices made out of graphene. Currentdifficulties with respect to this goal lie in that conventionalelectronic operations require the ability to completelypinch off the charge transport on demand. Although theelectric field effect is impressive in graphene [2], the ex-istence of a minimum of conductivity poses a seriousobstacle towards desirable on/off ratios. A gapped spec-trum would certainly be instrumental. The presence of agap is implicitly related to the problem of electron con-finement, which for Dirac fermions is not easily achievableby conventional means (like electrostatic potential wells)[3]. Geometrical confinement has been achieved in gra-phene ribbons and dots [4,5], but the sensitivity of transportto the edge profile [6], and the inherent difficulty in thefabrication of such microstructures with sharply definededges remains a problem.

    The ultimate goal would be an all-graphene circuit. Thiscould be achieved by taking a graphene sheet and pattern-ing the different devices and leads by means of appropriatecuts that would generate leads, ribbons, dots, etc. Thispaper cutting electronics can have serious limitationswith respect to reliability, scalability, and is prone todamaging and inducing disorder in the graphene sheet[7]. Therefore, in keeping with the paper art analogy, wepropose an alternative origami electronics [8].

    We show here that all of the characteristics of grapheneribbons and dots (viz. geometrical quantization, 1D chan-nels, surface modes) might be locally obtained by pattern-ing, not graphene, but the substrate on which it rests. Theessential aspect of our approach is the generation of strainin the graphene lattice capable of changing the in-planehopping amplitude in an anisotropic way. This can beachieved by means of appropriate geometrical patterns ina homogeneous substrate (grooves, creases, steps, orwells), by means of a heterogeneous substrate in which

    different regions interact differently with the graphenesheet, generating different strain profiles [Fig. 1(b)].Another design alternative consists in depositing grapheneonto substrates with regions that can be controllablystrained on demand [9], or by exploring substrates withthermal expansion heterogeneity. Through a combinationof folding and/or clamping a graphene sheet onto suchsubstrates, one might generate local strain profiles suitablefor the applications discussed in detail below, while pre-serving a whole graphene sheet.The remainder of the Letter is dedicated to showing how

    strain only can be used as a means of achieving (i) directiondependent tunneling, (ii) beam collimation, (iii) con-finement, (iv) the spectrum of an effective ribbon, (v) 1Dchannels, and (vi) surface modes.Model.Within a tight-binding formulation of the elec-

    tronic motion [10], effects of in-plane strain can be cap-tured, to leading order, by considering the changes innearest-neighbor hopping amplitude, t. We writetRi;n t !tRi;n, and treat the space dependentstrain-induced modulation, !t, as a perturbation (t %3 eV). It is straightforward to show [10] that, for smoothperturbations, the low energy Hamiltonian is

    H vFZ

    dr!y! &

    !p' 1vFA

    "0

    0 '! &!p 1vF A

    "24

    35!;

    (1)

    valid near the valleys K and K0 in the Brillouin zone, with

    FIG. 1 (color online). (a) Lattice orientation considered in thetext. Thicker bonds have perturbed hopping. (b) Artistic depic-tion of a substrate (S) patterned with folds (F), trenches, dots andwells (A), upon which rests a graphene sheet (G).

    PRL 103, 046801 (2009) P HY S I CA L R EV I EW LE T T E R Sweek ending24 JULY 2009

    0031-9007=09=103(4)=046801(4) 046801-1 ! 2009 The American Physical Society

    Eletrnica origami

    Ultracapacitores

    46Wednesday, January 19, 2011

  • Campus Party BR 2011 @tgrappoport Tatiana G. Rappoport

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    IBM

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    Sensores de gs

    Strain Engineering of Graphenes Electronic Structure

    Vitor M. Pereira and A.H. Castro NetoDepartment of Physics, Boston University, 590 Commonwealth Avenue, Boston, Massachusetts 02215, USA

    (Received 13 February 2009; published 20 July 2009)

    We explore the influence of local strain on the electronic structure of graphene. We show that strain can

    be easily tailored to generate electron beam collimation, 1D channels, surface states, and confinement.

    These can be seen as basic elements for all-graphene electronics which, by suitable engineering of local

    strain profiles, could be integrated on a single graphene sheet. In addition this proposal has the advantage

    that patterning can be made on substrates rather than on graphene, thereby protecting the integrity of the

    latter.

    DOI: 10.1103/PhysRevLett.103.046801 PACS numbers: 81.05.Uw, 73.90.+f, 85.30.Mn

    Notwithstanding its atomic thickness, graphene sheetshave been shown to accommodate a wealth of remarkablefundamental properties, and to hold sound prospects in thecontext of a new generation of electronic devices andcircuitry [1]. One exciting prospect about graphene isthat, not only can we have extremely good conductors,but also most active devices made out of graphene. Currentdifficulties with respect to this goal lie in that conventionalelectronic operations require the ability to completelypinch off the charge transport on demand. Although theelectric field effect is impressive in graphene [2], the ex-istence of a minimum of conductivity poses a seriousobstacle towards desirable on/off ratios. A gapped spec-trum would certainly be instrumental. The presence of agap is implicitly related to the problem of electron con-finement, which for Dirac fermions is not easily achievableby conventional means (like electrostatic potential wells)[3]. Geometrical confinement has been achieved in gra-phene ribbons and dots [4,5], but the sensitivity of transportto the edge profile [6], and the inherent difficulty in thefabrication of such microstructures with sharply definededges remains a problem.

    The ultimate goal would be an all-graphene circuit. Thiscould be achieved by taking a graphene sheet and pattern-ing the different devices and leads by means of appropriatecuts that would generate leads, ribbons, dots, etc. Thispaper cutting electronics can have serious limitationswith respect to reliability, scalability, and is prone todamaging and inducing disorder in the graphene sheet[7]. Therefore, in keeping with the paper art analogy, wepropose an alternative origami electronics [8].

    We show here that all of the characteristics of grapheneribbons and dots (viz. geometrical quantization, 1D chan-nels, surface modes) might be locally obtained by pattern-ing, not graphene, but the substrate on which it rests. Theessential aspect of our approach is the generation of strainin the graphene lattice capable of changing the in-planehopping amplitude in an anisotropic way. This can beachieved by means of appropriate geometrical patterns ina homogeneous substrate (grooves, creases, steps, orwells), by means of a heterogeneous substrate in which

    different regions interact differently with the graphenesheet, generating different strain profiles [Fig. 1(b)].Another design alternative consists in depositing grapheneonto substrates with regions that can be controllablystrained on demand [9], or by exploring substrates withthermal expansion heterogeneity. Through a combinationof folding and/or clamping a gra