Tight-binding model and direct-gap/indirect-gap transition in single-layer and multi-layer MoS$_2$

TL;DR

This paper develops a tight-binding model for MoS$_2$ that explains the transition from direct to indirect band gap as layers increase, aiding understanding of electronic properties in layered semiconductors.

Contribution

The paper introduces a simple yet effective tight-binding model that captures the direct-indirect gap transition in multilayer MoS$_2$ and similar materials.

Findings

Model reproduces multilayer electronic properties from single-layer parameters.

Transition from direct to indirect gap explained by interlayer orbital splitting.

Model allows analytical study of strain and finite-size effects.

Abstract

In this paper we present a paradigmatic tight-binding model for single-layer as well as for multi-layered semiconducting MoS$_2$ and similar transition metal dichalcogenides. We show that the electronic properties of multilayer systems can be reproduced in terms of a tight-binding modelling of the single-layer hopping terms by simply adding the proper interlayer hoppings ruled by the chalcogenide atoms. We show that such tight-binding model permits to understand and control in a natural way the transition between a direct-gap band structure, in single-layer systems, to an indirect gap in multilayer compounds in terms of a momentum/orbital selective interlayer splitting of the relevant valence and conduction bands. The model represents also a suitable playground to investigate in an analytical way strain and finite-size effects.