Minimal d-Band Model for the Optical Susceptibility of Non-Centrosymmetric Monolayer Transition Metal Dichalcogenides

Abstract

The optical response of two-dimensional materials has been customarily calculated {\it ab initio} using plane waves basis and the full Bloch wavefunction, without separating the most important orbital contributions. In the family of monolayer transition metal dichalcogenides lacking inversion symmetry, we take advantage of the mostly $d-$orbital content of the Bloch bands around the semiconductor gap to reduce the calculation of their linear and quadratic optical susceptibilities to a very minimal model that includes only three energy bands. As the Bloch wavefunction determines the microscopic response to external fields, this simple approach reproduces well first principles calculations up to roughly 2 eV above the band gap. This could be the starting point for the inclusion of many-body effects with only a few energy bands in a numerically inexpensive way.