Pierre A. Pantaleón, Tony Low, Francisco Guinea

Recent experiments have measured local uniaxial strain fields in twisted bilayer graphene (TBG). Our calculations found that the finite Berry curvature generated by breaking the sublattice symmetry and the band proximity between narrow bands in these TBG induces a giant Berry dipole of order 10\,nm or larger. The large Berry dipole leads to transverse topological non-linear charge currents which dominates over the linear bulk valley current at experimentally accessible crossover in-plane electric field of $\sim 0.1 {\rm mV} / \mu \rm{m}$. This anomalous Hall effect, due to Berry dipole, is strongly tunable by the strain parameters, electron fillings, gap size, and temperature.