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

TL;DR

This paper analyzes Landau levels and Shubnikov-de Haas oscillations in monolayer transition metal dichalcogenides using a multi-band theory, revealing how magnetic field, doping, and band structure influence magnetotransport properties.

Contribution

It introduces a comprehensive theoretical framework combining multi-band k·p theory and magnetotransport calculations to explain experimental observations in monolayer TMDs.

Findings

Landau levels follow a harmonic oscillator spectrum with valley degeneracy breaking.

Doping and spin-splitting significantly affect magnetoconductance oscillations.

Theoretical results align with recent experimental data on MoS₂ and WSe₂.

Abstract

We study the Landau level spectrum using a multi-band $\mathbf{k}\cdot\mathbf{p}$ theory in monolayer transition metal dichalcogenide semiconductors. We find that in a wide magnetic field range the Landau levels 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 Landau level 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 Landau levels affect the magnetoconductance oscillations. Motivated by recent experiments we consider monolayer MoS$_2$ and WSe$_2$ 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 (Reference [18]) using the theoretical approach we have developed.