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

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.