k⋅p theory for two-dimensional transition metal dichalcogenide semiconductors

Abstract

We present k⋅p Hamiltonians parametrised by {\it ab initio} density functional theory calculations to describe the dispersion of the valence and conduction bands at their extrema (the K, Q, Γ, and M points of the hexagonal Brillouin zone) in atomic crystals of semiconducting monolayer transition metal dichalcogenides. We review the parametrisation of the essential parts of the k⋅p Hamiltonians for MoS2, MoSe2, WS2, and WSe2, including the spin-splitting and spin-polarisation of the bands, and we discuss the vibrational properties of these materials. We then use k⋅p theory to analyse optical transitions in two-dimensional transition metal dichalcogenides over a broad spectral range that covers the Van Hove singularities in the band structure (the M points). We also discuss the visualisation of scanning tunnelling microscopy maps.