Green's function approach to edge states in transition metal dichalcogenides

Abstract

The semiconducting two-dimensional transition metal dichalcogenides MX 2 show an abundance of onedimensional 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'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'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. Aside from 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 11-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.

Electronic Band Structure of Transition Metal Dichalcogenides from Ab Initio and Slater–Koster Tight-Binding Model

“…The advantage of a tight-binding description with respect to first-principles methods is that it provides a simple starting point for the further inclusion of many-body electron-electron interaction, external strains, as well as of the dynamical effects of the electron-lattice interaction. Tight-binding approaches are often more convenient than ab initio methods for investigating systems involving a very large number of atoms [26], disordered and inhomogeneous samples [29], strained and/or bent samples [30,31], materials nanostructured in large scales (nanoribbons [32,33], ripples [34]) or in twisted multilayer materials. The aim of the present paper is twofold.…”

Symmetries and hybridization in the indirect interaction between magnetic moments inMoS2nanoflakes

“…Finite TMD samples exhibit highly localized states near the edges of the flake, [60][61][62][63][64] resulting in noncolinear and tunable long range interactions when the impurities sit at these edges, and with slow decay with the impurity separation. 41,42 The plaquette hybridization geometry has not yet been reported on TMDs.…”

Van der Waals Contact to 2D Semiconductors with a Switchable Electric Dipole: Achieving Both n‐ and p‐Type Ohmic Contacts to Metals with a Wide Range of Work Functions

“…First, the pushback effect makes electrons push back into the metal, resulting in the work‐function decrease, which is a general phenomenon in the physisorption of 2D semiconductors on metals 56. In Mo 2 CF 2 ‐pS junctions, the pushback effect is more apparent in ML‐B (Mo 2 CF 2 contacting to pS (00‐1) surface, the relatively high work‐function model in Figure 2b) than ML‐A 57. Second, the built‐in electrical field of pS also makes a contribution to charge transfer/redistribution at the metal‐pS interface.…”

“…[56] In Mo 2 CF 2 -pS junctions, the pushback effect is more apparent in ML-B (Mo 2 CF 2 contacting to pS (00-1) surface, the relatively high work-function model in Figure 2b) than ML-A. [57] Second, the builtin electrical field of pS also makes a contribution to charge transfer/redistribution at the metal-pS interface. In the ML-A system, the built-in dipole promote electron from metal to pS at interface (Figure 3e).…”