Two-dimensional to bulk crossover of the WSe$_2$ electronic band structure

TL;DR

This study investigates the transition of the electronic band structure of WSe$_2$ from two-dimensional to three-dimensional behavior as the number of layers increases, using experimental and theoretical methods.

Contribution

It provides a detailed experimental and theoretical analysis of the 2D to 3D crossover in WSe$_2$, highlighting the evolution of band dispersion with layer number.

Findings

Bulk-like dispersion nearly achieved at 6 layers

Discrete electronic states increase with more layers

Theoretical models successfully reproduce experimental results

Abstract

Transition Metal Dichalcogenides (TMD) are layered materials obtained by stacking two-dimensional sheets weakly bonded by van der Waals interactions. In bulk TMD, band dispersions are observed in the direction normal to the sheet plane (z-direction) due to the hybridization of out-of-plane orbitals but no kz-dispersion is expected at the single-layer limit. Using angle-resolved photoemission spectroscopy, we precisely address the two-dimensional to three-dimensional crossover of the electronic band structure of epitaxial WSe$_2$ thin films. Increasing number of discrete electronic states appears in given kz-ranges while increasing the number of layers. The continuous bulk dispersion is nearly retrieved for 6-sheet films. These results are reproduced by calculations going from a relatively simple tight-binding model to a sophisticated KKR-Green's function calculation. This two-dimensional system is hence used as a benchmark to compare different theoretical approaches.