Green${}^{\prime }$s function approach to edge states in transition metal dichalcogenides

Abstract

The semiconducting two-dimensional transition metal dichalcogenides MX${}_2$ show an abundance of one-dimensional metallic edges and grain boundaries. Standard techniques for calculating edge states typically model nanoribbons, and require the use of supercells. In this paper we formulate a Green${}^{\prime }$s function technique for calculating edge states of (semi-)infinite two-dimensional systems with a single well-defined edge or grain boundary. We express Green${}^{\prime }$s functions in terms of Bloch matrices, constructed from the solutions of a quadratic eigenvalue equation. The technique can be applied to any localized basis representation of the Hamiltonian. Here we use it to calculate edge states of MX${}_2$ monolayers by means of tight-binding models. Besides the basic zigzag and armchair edges, we study edges with a more general orientation, structurally modifed edges, and grain boundaries. A simple three-band model captures an important part of the edge electronic structures. An eleven-band model comprising all valence orbitals of the M and X atoms, is required to obtain all edge states with energies in the MX${}_2$ band gap. Here states of odd symmetry with respect to a mirror plane through the layer of M atoms have a dangling-bond character, and tend to pin the Fermi level.

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• Electronic Band Structure of Transition Metal Dichalcogenides from Ab Initio and Slater-Koster Tight-Binding Model
• Tomonaga-Luttinger liquid in a box: electrons confined within MoS${}_2$ mirror twin boundaries
• The Sign of Three: Spin/Charge Density Waves at the Boundaries of Transition Metal Dichalcogenides
• Symmetries and hybridization in the indirect interaction between magnetic moments in MoS${}_2$ nanoflakes
• Floquet Spectrum and Two-Terminal Conductance of a Transition Metal Dichalcogenide Ribbon under a Circularly Polarized Laser Field
• One-dimensional electronic instabilities at the edges of $Mo{S}_2$
• Atomically Thin Metallenes at the Edge
• Fractional quantum anomalous Hall phase for Raman superarray of Rydberg atoms
• Switchable valley functionalities of an $n-n^{-}-n$ junction in 2D semiconductors
• Efficient algorithms for surface density of states in topological photonic and acoustic systems