Wannier based analysis of the direct-indirect bandgap transition by stacking MoS$_2$ layers

TL;DR

This paper uses Wannier-based analysis combined with first-principles calculations to elucidate the microscopic mechanisms behind the direct-indirect bandgap transition in layered MoS$_2$, emphasizing the roles of various interlayer orbital couplings.

Contribution

It reveals that both out-of-plane and in-plane interlayer sulfur orbital couplings are essential for accurately describing the bandgap transition in MoS$_2$, advancing understanding of its electronic properties.

Findings

Interlayer $p_z$--$p_z$ coupling is a key factor in the bandgap transition.

Additional $p_z$--$p_x$ and $p_z$--$p_y$ couplings are necessary for a complete description.

Both out-of-plane and in-plane orbital interactions influence the electronic structure of multilayer MoS$_2$.

Abstract

Molybdenum disulfide (MoS$_2$), a layered van der Waals material, has attracted considerable attention as a promising alternative to graphene for applications in field-effect transistors and nanophotonic devices because of its sizable band gap, high carrier mobility, large on/off ratio, and strong photoluminescence efficiency. A particularly intriguing property of MoS$_2$ is the transition of its band gap character with layer thickness: while the monolayer exhibits a direct gap, the band gap becomes indirect in multilayer and bulk forms.In this study, we clarify the microscopic mechanism underlying this transition. Focusing on the roles of atomic orbitals and interlayer interactions, we perform an analysis combining first-principles calculations with a Wannier-based model. Although interlayer $p_z$--$p_z$ coupling between neighboring sulfur atoms has been recognized as a key factor in this transition, we find that a complete quantitative description additionally requires interlayer $p_z$--$p_x$ and $p_z$--$p_y$ couplings between neighboring sulfur atoms. These findings highlight the importance of both out-of-plane and in-plane orbital contributions in governing the electronic structure of layered MoS$_2$, providing deeper insight into its band gap engineering for future device applications.