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!