Bandwidth-Limited Critical Currents in Electrically Tunable Moiré Bands

Moiré superlattices host narrow minibands whose bandwidth governs correlated and topological phases. Here, we demonstrate that the bandwidth also sets the critical current for the onset of out-of-equilibrium transport. In bilayer graphene aligned to hexagonal boron nitride, we explore the high-current transport regime as we continuously flatten the valence miniband using an out-of-plane displacement field. We observe a significant reduction in the critical current, which is captured by a minimal analytical model and corresponds to the calculated narrowing of the miniband. Moreover, by comparing distinct moiré platforms, we show that the scaling between critical current and bandwidth is a universal feature of graphene superlattices. Our results reveal a direct link between miniband dispersion and high-current transport, and establish this regime as a fast and accessible electrical probe of bandwidth evolution.