Influence of atomic relaxations on the moir\'{e} flat band wavefunctions in antiparallel twisted bilayer WS$_{\text{2}}$

TL;DR

This study combines experimental STM imaging and spectroscopy with theoretical DFT calculations to explore how atomic relaxations influence the localization of flat valence band wavefunctions in twisted bilayer WS₂, highlighting substrate effects.

Contribution

It reveals that atomic relaxations significantly affect the localization of flat bands, demonstrating the importance of substrate and temperature in twisted bilayer TMDs.

Findings

Localized electronic states near valence band onset.

Relaxed DFT calculations match experimental localization.

Atomic relaxations alter flat band wavefunction localization.

Abstract

Twisting bilayers of transition metal dichalcogenides (TMDs) gives rise to a periodic moir\'{e} potential resulting in flat electronic bands with localized wavefunctions and enhanced correlation effects. In this work, scanning tunneling microscopy is used to image a WS$_{2}$ bilayer twisted approximately $3^{\circ}$ off the antiparallel alignment. Scanning tunneling spectroscopy reveals the presence of localized electronic states in the vicinity of the valence band onset. In particular, the onset of the valence band is observed to occur first in regions with a Bernal stacking in which S atoms are located on top of each other. In contrast, density-functional theory calculations on twisted bilayers which have been relaxed in vacuum predict the highest lying flat valence band to be localized in regions of AA' stacking. However, agreement with the experiment is recovered when the calculations are carried out on bilayers in which the atomic displacements from the unrelaxed positions have been reduced reflecting the influence of the substrate and finite temperature. This demonstrates the delicate interplay of atomic relaxations and the electronic structure of twisted bilayer materials.