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

TL;DR

This paper develops and parametrizes $oldsymbol{k}oldsymbol{ullet}oldsymbol{p}$ Hamiltonians for monolayer transition metal dichalcogenides using ab initio calculations, enabling detailed analysis of their electronic, vibrational, and optical properties.

Contribution

It provides a comprehensive $oldsymbol{k}oldsymbol{ullet}oldsymbol{p}$ model for TMD monolayers, including spin effects and optical transition analysis, based on first-principles data.

Findings

Parametrized $oldsymbol{k}oldsymbol{ullet}oldsymbol{p}$ Hamiltonians for MoS$_2$, MoSe$_2$, WS$_2$, and WSe$_2$.

Analysis of optical transitions across broad spectral ranges, including Van Hove singularities.

Insights into vibrational properties and STM map visualization of TMD monolayers.

Abstract

We present $\mathbf{k}\cdotp\mathbf{p}$ Hamiltonians parametrised by {\it 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, and we discuss the vibrational properties of these materials. We then use $\mathbf{k}\cdotp\mathbf{p}$ theory to analyse optical transitions in two-dimensional transition metal dichalcogenides over a broad spectral range that covers the Van Hove singularities in the band structure (the $M$ points). We also discuss the visualisation of scanning tunnelling microscopy maps.