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

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.

11 pages, 6 figures

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• Edge states in dichalcogenide nanoribbons and triangular quantum dots
• Green${}^{\prime }$s function approach to edge states in transition metal dichalcogenides
• Edge states and spin-valley edge photocurrent in transition metal dichalcogenide monolayers
• Collective excitations in two-component one-dimensional massless Dirac plasma
• SQUID pattern disruption in transition metal dichalcogenide Josephson junctions due to non-parabolic dispersion of the edge states
• Topological nature of in-gap bound states in disordered large-gap monolayer transition metal dichalcogenides