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

We present 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 Hamiltonians for MoS 2 , MoSe 2 , MoTe 2 , WS 2 , WSe 2 , and WTe 2 , including the spin-splitting and spin-polarization of the bands, and we briefly review the vibrational properties of these materials. We then use 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.