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

We present k⋅p Hamiltonians parametrized by 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 (TMDCs). We discuss the parametrization of the essential parts of the k⋅p Hamiltonians for MoS2, MoSe2, MoTe2, WS2, WSe2, and WTe2, including the spin-splitting and spin-polarization of the bands, and we briefly review the vibrational properties of these materials. We then use k⋅p theory to analyse optical transitions in two-dimensional TMDCs over a broad spectral range that covers the Van Hove singularities in the band structure (the M points). We also discuss the visualization of scanning tunnelling microscopy maps