Effect of Berry Phase on Nonlinear Response of Two-dimensional Fermions

We develop a theory of nonlinear response to an electric field of two-dimensional (2D) fermions with topologically non-trivial wave functions characterized by the Berry phase $\Phi_n = n \pi, n = 1,2,...$. In particular, we find that owing to suppression of backscattering at odd $n$, Hall field-induced resistance oscillations, which stem from elastic electron transitions between Hall field-tilted Landau levels, are qualitatively distinct from those at even $n$: their amplitude decays with the electric field and their extrema are phase-shifted by a quarter cycle. The theory unifies the cases of graphene ($n = 1$) and graphite bilayer ($n = 2$) with the case of conventional 2D electron gas ($n = 0$) and suggests a new method to probe backscattering in topological 2D systems.