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

Abstract

We derive the boundary conditions for ${\mathrm{MoS}}_{2}$ and similar transition-metal dichalcogenide honeycomb (2H polytype) monolayers with the same type of $\mathbf{k}\ifmmode\cdot\else\textperiodcentered\fi{}\mathbf{p}$ Hamiltonian within the continuum model around the K points. In an effective two-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 $2\ensuremath{\pi}$. We analyze the edge states and their dispersion relation in ${\mathrm{MoS}}_{2}$ in particular, and we find good agreement with the results of previous density functional theory calculations for various edge types.