Electronic and optical properties of two-dimensional InSe from a DFT-parameterized tight-binding model

We present a tight-binding (TB) model and $\mathbf{k}\cdot \mathbf{p}$ theory for electrons in monolayer and few-layer InSe. The model is constructed from a basis of all $s$ and $p$ valence orbitals on both indium and selenium atoms, with tight-binding parameters obtained from fitting to independently computed density functional theory (DFT) band structures for mono- and bilayer InSe. For the valence and conduction band edges of few-layer InSe, which appear to be in the vicinity of the $\mathrm{\Gamma }$ point, we calculate the absorption coefficient for the principal optical transitions as a function of the number of layers, $N$. We find a strong dependence on $N$ of the principal optical transition energies, selection rules, and optical oscillation strengths, in agreement with recent observations \cite{Bandurin2016}. Also, we find that the conduction band electrons are relatively light ($m\propto 0.14-0.18m_e$), in contrast to an almost flat, and slightly inverted, dispersion of valence band holes near the $\mathrm{\Gamma }$-point, which is found for up to $N\propto 6$.