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, Gamma, 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.