Non-linear electron transport in two-dimensional moiré superlattices.

Graphene based moire superlattices represent a new class of solid-state systems with exceptional electronic properties. In the linear response regime, their versatile properties have allowed access to rich plethora of phenomena including Hofstadter butterflies, strong electron correlations and even topological physics. In this work, we take the first steps to understand their behaviour in the non-linear regime. We perform high-field quantum transport measurements in a variety of graphene based moire superlattices, including monolayer graphene aligned to hBN and twisted bilayer graphene close to the magic angle (0.73 + 1.23 degree). In all the studied systems, we find non-linear transport is governed by the shift of the Fermi-surface within the superlattice mini-brillouin zones. In particular, we observe a set of sharp peaks in the differential resistivity that signals the on-set of electron-hole particle creation by the electric field. In addition, we observe a strongly non-linear Hall effect that correlates with the differential resistivity and even changes sign. Our work provides the first insights into non-linear electron transport phenomena in twisted graphene moire superlattices.