$\mathbf{k}\cdotp\mathbf{p}$ theory for two-dimensional transition metal dichalcogenide semiconductors

We present $\mathbf{k}\cdotp\mathbf{p}$ Hamiltonians (for a review see [1]) parametrised 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. We review the parametrisation of the essential parts of the $\mathbf{k}\cdotp\mathbf{p}$ Hamiltonians for MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$, including the spin-splitting and spin-polarisation of the bands We use $\mathbf{k}\cdotp\mathbf{p}$ theory to analyse: i) optical transitions in two-dimensional transition metal dichalcogenides over a broad spectral range; ii) to discuss magnetotransport properties of the charge carriers in the $K$ and $-K$ valleys. \newline [1] A. Korm\'anyos, G. Burkard et al, arXiv:1410.6666