Disorder-induced symmetry breaking in moiré bands of marginally twisted bilayer MoS$_2$
Twisted transition-metal dichalcogenides host highly tunable moiré 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 ($θ\approx 0.95^\circ$) 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 moiré 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 moiré materials at the nanoscale.