Disorder-induced symmetry breaking in moir\'e bands of marginally twisted bilayer MoS$_2$

TL;DR

This study reveals how electrostatic disorder significantly influences the electronic properties of marginally twisted bilayer MoS₂, demonstrating the importance of disorder effects in moiré materials through combined experimental and theoretical analysis.

Contribution

It provides the first detailed investigation of electrostatic disorder effects on moiré bands in twisted bilayer MoS₂ using scanning tunneling spectroscopy and continuum modeling.

Findings

Disorder causes energy shifts of about 15 meV in band onset energies.

Spatially correlated disorder aligns with a background charge density of 10^{11} cm^{-2}.

Disorder effects are crucial for understanding the electronic structure at the nanoscale.

Abstract

Twisted transition-metal dichalcogenides host highly tunable moir\'e potentials, flat bands, and correlated electronic phases, yet the role of disorder in shaping these emergent properties remains largely unresolved. Using scanning tunneling spectroscopy, we investigate the impact of electrostatic disorder on the electronic structure of marginally twisted ($\theta \approx 0.95^\circ$) bilayer MoS$_2$. Differences of 15 meV in the onset energies of the valence and conduction bands between MX- and XM-stacked regions are observed and are unexpected based on symmetry considerations. We further observe spatially correlated disorder in the band onset energy that is consistent with a background random charge density of a few $10^{11}\,\mathrm{cm}^{-2}$. Continuum model calculations for twisted MoS$_2$ reveal dramatic changes in the low-energy moir\'e bands in response to an electric displacement field, in quantitative agreement with experiment. Moreover, the calculated local density of states including disorder broadening reproduces the experimental observations only when structural relaxation is taken into account. These results highlight the critical role of electrostatic disorder in determining the electronic structure of moir\'e materials at the nanoscale.