Non-Classical Longitudinal Magneto-Resistance in...
Transcript of Non-Classical Longitudinal Magneto-Resistance in...
Stefan Heun
NEST, Istituto Nanoscienze-CNR and
Scuola Normale Superiore, Pisa, Italy
Non-Classical Longitudinal Magneto-Resistance
in Anisotropic Black Phosphorus
S.Heun
Oulin Yu
M. Peruzzini
M. Petrescu
M. Carrega
G. Gervais T. Szkopek N. Hemsworth
M. Caporali
D. Graf
F. Telesio
V. Tayari
M. Serrano-Ruiz
S. Roddaro
W. Dickerson
S. Xiang
A. Ienco
F. Beltram
Funding:
Black phosphorus
Layered structure with orthorhombic symmetry
J. R. Brent et al., Chem. Commun. 50 (2014) 13338.
Cell parameters a=3.13Å b=10.47Å c=4.37Å
Black phosphorus
• In 1914 first successful synthesis
(Bridgman), and in 2007 synthesis at
atmospheric pressure (Lange, Nilges)
• Strong crystalline in-plane anisotropy
• p-type semiconductor: 0.3eV direct
band gap and high hole mobility (64,000
cm2/Vs @ 20 K)
• 1983 (Narita): n-type doping by Te
• Vibrational modes of the crystal are
Raman active
A. Morita, Appl. Phys. A 39 (1986) 227. F. Xia et al, Nat Comm 5 (2014) 4458.
Black phosphorus
First few layer bP isolation
and ultra-thin bP FET reported
The renaissance of black
phosphorus
First few layer bP isolation
and ultra-thin bP FET reported
L. Li et al, Nature Nanotech. 9 (2014) 372 (Y. Zhang group); H. Liu et al, ACS Nano 8 (2014) 4033 (P. Ye group); A. Castellanos-Gomez et al, 2D Materials 1 (2014) 025001; V. Tayari et al, Nat. Comm. 6 (2015) 7702 (McGill group); N. Gillren et al, 2D Materials 2 (2014) 011001 (J. Lau group); X. Chen et al, Nat. Comm. 6 (2015) 7315 (N. Wang group)
The renaissance of black
phosphorus
• Direct band-gap tunable with layer number
S. Das et al., Nano Lett. 14 (2014)
The renaissance of black
phosphorus
• Direct band-gap tunable with layer number
• In-plane anisotropy of optical and transport
properties
F. Xia et al., Nat. Comm. 5 (2014)
Dephasing in strongly
anisotropic black phosphorus
bP Field Effect Transistor
Rxx: 1-2 Rxy: 1-3
Flake thickness: 65 ± 2 nm
PMMA MMA Ti/Au contacts bP flake HMDS SiO2 thermal oxide Si
N. Hemsworth et al., Phys. Rev. B 94, 245404 (2016).
Transport Characterization
• p ~ Vg for Vg < -30 V
• p = 1013 cm-2 for Vg = -30 V
• Field-effect mobility µ: 300 cm2/Vs at Vg = -70 V
• Negligible T-dependence in µ
for 0.26 K < T < 20 K
N. Hemsworth et al., Phys. Rev. B 94, 245404 (2016).
Magnetotransport
N. Hemsworth et al., Phys. Rev. B 94, 245404 (2016).
T = 300 mK
Weak Localization
T = 0.26 K
N. Hemsworth et al., Phys. Rev. B 94, 245404 (2016).
Scattering Lengths
BL2 = h4e
𝐿𝜑,𝑚𝑎𝑥 = 55 𝑛𝑚
N. Hemsworth et al., Phys. Rev. B 94, 245404 (2016).
Scattering Lengths
• Ballistic transport: 𝜏𝜑 ∝ 𝑇−2
• Diffusive transport (𝜏0 < 𝜏𝜑):
Dephasing length vs. inelastic scattering time:
𝐿𝜑 = 𝐷𝜏𝜑 with D diffusion coefficient
𝜏𝜑 ∝ 𝑇−1 or 𝐿𝜑 ∝ 𝑇−12
Lin and Bird, Jour. Phys. Cond. Mat. 14, R501, (2002)
Scattering Lengths
Saturation most likely due to dynamical impurities.
N. Hemsworth et al., Phys. Rev. B 94, 245404 (2016).
Scattering Lengths
Saturation most likely due to dynamical impurities.
𝐿𝜑 does not
follow a 𝑇−12
behaviour.
N. Hemsworth et al., Phys. Rev. B 94, 245404 (2016).
Quasi-1D systems
Comparison with quasi-1D wires
𝜏𝜑 ∝ 𝑇−2 3
𝐿𝜑 ∝ 𝑇−1 3
D. Natelson et al. PRL 86 (2009): quasi-1D:
𝐿𝜑, 𝐿𝑇 > 𝑤, 𝑡
width w thickness t
0.1 1 10
1E-12
1E-11
(s
)
T (K)
T-2/3
Natelson
(sample A)
Natelson
(sample B)
0.1 1 10
1E-12
1E-11
(s
)
T (K)
T-2/3
Natelson
(sample A)
Natelson
(sample B)
This work
(Vg=-80V)
N. Hemsworth et al., Phys. Rev. B 94, 245404 (2016).
Non-classical Longitudinal
Magneto-Resistance
bP FET device
(16±1) nm thick bP flake
Two top gates TG1 and TG2 fabricated with a
combination of POx and Al2O3 (cf. W.
Dickerson et al., APL 112, (2018) 173101)
n = 2.2 x 1012 cm-2 and µ=83 cm2/(Vs) at 1.5
K, 11.4 T
20 μm
S
D
-1 0 1
200
300
400
500
600
R (
k
)VTG2 (V)
TG1
TG2
F. Telesio et al., arXiv:1808.00858
microscope
objective
Sample
Polarizer
(half wavelength retarder)
Side view
Laser beam
Laser polarization
mirror
Detector
Rayleigh rejection filters
Crystal orientation:
polarized Raman
F. Telesio et al., arXiv:1808.00858
Crystal orientation:
polarized Raman
-180 -90 0
5
10
15
20
A2 g
R
am
an
In
ten
sit
y (
a.
u.)
(°)
20 μm
φ polarization
S
D
TG1
TG2
F. Telesio et al., arXiv:1808.00858
In-plane magnetotransport:
the experimental setup
20 μm
φ B
S
D
TG1
TG2
Hybrid 45 T magnet Tallahassee, USA
The sample is mounted on a rotator and it rotates in the plane of magnetic field.
F. Telesio et al., arXiv:1808.00858
20 μm
φ B
S
D
300mK, VTG2=-1V
In plane magnetotransport
F. Telesio et al., arXiv:1808.00858
In plane magnetotransport
The conventional model based on Lorentz force cannot produce longitudinal magnetoresistance
LMR, since 𝑣 ∥ 𝐵
𝐹 = 𝑞(𝐸 + 𝑣 × 𝐵)
A longitudinal magnetoresistance has been measured in 1994 in bulk bP but never been understood [T. Strutz et al, Physica B 194 (1994) 1185].
300mK, VTG2=-1V
0 10 20 30 40 50-0.04
0.00
0.04
0.08
0.12
(R(B
)-R
(0))
/R(0
)
Magnetic field (T)
𝐵 ⊥ 𝐼, 𝜑 = −90°
TMR
𝐵 ∥ 𝐼, 𝜑 = 0°
LMR
F. Telesio et al., arXiv:1808.00858
[2] N. Iwasaki et al, Chemistry Lett. 14 (1985) 119; T.-H. Lee et al, Phys. Stat. Sol. RRL 10 (2016) 819, S. J. Choi et al, Nano Letters 16 (2016) 3969, G. Long et al Nanotechnology 29 (2018) 035204 ; N. Hemsworth et al, PRB 94 (2016) 245404.
300mK, VTG2=-1V
0 10 20 30 40 50-0.04
0.00
0.04
0.08
0.12
(R(B
)-R
(0))
/R(0
)
Magnetic field (T)
𝐵 ∥ 𝐼, 𝜑 = 0°
𝐵 ⊥ 𝐼, 𝜑 = −90°
bP has an elliptical in-plane Fermi surface
Elastic mean free path:
𝑙𝑒,𝑧𝑧 = 3.2 𝑛𝑚
Ioffe-Regel criterion:
𝛼 = 𝑙𝑒,𝑧𝑧𝑘𝐹,𝑧𝑧 = 1.9
Close to strong localization
Consistent with previous literature on disordered/localized bP [2]
In plane magnetotransport:
low field regime
TMR
LMR
LMR can arise in case of Fermi surface anisotropy [3]
Its sign can be negative or positive (and it can change) for different scattering mechanisms, from short range to long range scattering [4]
This picture still holds in a
semiclassical regime [5]
0 10 20 30 40 50-0.04
0.00
0.04
0.08
0.12
(R(B
)-R
(0))
/R(0
)
Magnetic field (T)
In plane magnetotransport:
high field regime
300mK, VTG2=-1V
𝐵 ⊥ 𝐼, 𝜑 = −90°
TMR
𝐵 ∥ 𝐼, 𝜑 = 0°
LMR
[3] Pal and Maslov, PRB 81 (2010) 214438 [4] Goswami, Pixley and Das Sarma, PRB 92 (2015) 075205
[5] Son and Spivak, PRB 88 (2013) 104412
Conclusions
• Weak localization observed in a bP FET
– T-dependence of 𝐿𝜑 close to quasi-1D
– We attribute this to the strong in-plane anisotropy of bP
• In-plane magnetoresistance of a bP FET
– The observed behavior was strongly anisotropic
– Fermi surface anisotropy, with the field rotating in the
plane where anisotropy is pronounced, plays a crucial role
in explaining this phenomenon
Thank you for your attention!