Boundary conditions for transition-metal dichalcogenide monolayers in the continuum model

TL;DR

This paper derives boundary conditions for transition-metal dichalcogenide monolayers like MoS2 within the continuum model, accounting for edge effects and reconstructions, and validates findings against DFT calculations.

Contribution

It introduces a linear edge constraint method for modeling edges in TMD monolayers, extending previous approaches used for graphene.

Findings

Edge states and dispersion relations are characterized for MoS2.

Different edge reconstructions can be described with a single scalar parameter.

Results agree well with density functional theory calculations.

Abstract

We derive the boundary conditions for MoS$_2$ and similar transition-metal dichalcogenide honeycomb (2H polytype) monolayers with the same type of $\mathbf{k}\!\cdot\!\mathbf{p}$ Hamiltonian within the continuum model around the K points. In an effective 2-band description, the electron-hole symmetry breaking quadratic terms are also taken into account. We model the effect of the edges with a linear edge constraint method that has been applied previously to graphene. Focusing mainly on zigzag edges, we find that different reconstruction geometries with different edge-atoms can generally be described with one scalar parameter varying between 0 and $2\pi$. We analyze the edge states and their dispersion relation in MoS$_2$ in particular, and we find good agreement with the results of previous density functional theory calculations for various edge types.