Landau levels and Shubnikov–de Haas oscillations in monolayer transition metal dichalcogenide semiconductors

Andor Kormányos,Guido Burkard,Péter Rakyta

doi:10.1088/1367-2630/17/10/103006

Abstract

We study the Landau level (LL) spectrum using a multi-band theory in monolayer transition metal dichalcogenide semiconductors. We find that in a wide magnetic field range the LL can be characterized by a harmonic oscillator spectrum and a linear-in-magnetic field term which describes the valley degeneracy breaking. The effect of the non-parabolicity of the band-dispersion on the LL spectrum is also discussed. Motivated by recent magnetotransport experiments, we use the self-consistent Born approximation and the Kubo formalism to calculate the Shubnikov–de Haas oscillations of the longitudinal conductivity. We investigate how the doping level, the spin-splitting of the bands and the broken valley degeneracy of the LLs affect the magnetoconductance oscillations. We consider monolayer MoS2 and WSe2 as concrete examples and compare the results of numerical calculations and an analytical formula which is valid in the semiclassical regime. Finally, we briefly analyze the recent experimental results (Cui et al 2015 Nat. Nanotechnol. 10 534) using the theoretical approach we have developed.

Highlights

Thin transition metal dichalcogenides semiconductors (TMDCs) [1,2,3] are recognized as a material system which, due to its finite band gap, may have a complementary functionality to graphene, the best known member of the family of atomically thin materials
We have shown that in a wide magnetic field range the effects of the trigonal warping in the band structure are not very important for the LL spectrum
The LL spectrum can be approximated by a harmonic oscillator spectrum and a linear-in-magntic field term which describes the valley degeneracy breaking (VDB)

Summary

Introduction

Thin transition metal dichalcogenides semiconductors (TMDCs) [1,2,3] are recognized as a material system which, due to its finite band gap, may have a complementary functionality to graphene, the best known member of the family of atomically thin materials. It was shown that in boron-nitride encapsulated mono- and few-layer MoS2 [18] and in few layer WSe2 [20] it was possible to measure the Shubnikov–de Haas (SdH) oscillations of the longitudinal resistance. Both of these developments are very significant and can provide complementary informations: the. Motivated by recent experiments in MoS2 [18] and WSe2 [20], we use the LL spectrum and the self-consistent Born approximation (SCBA) to calculate the SdH oscillations of the longitudinal conductance sxx. We point out the different scenarios that can occur depending on the doping level

LLs in monolayer TMDCs

LLs from an extended two-band model

SdH oscillations of longitudinal conductivity

Summary