Nonlinear magnetotransport theory and Hall induced resistance oscillations in graphene

Abstract

The quantum oscillations of nonlinear magnetoresistance in graphene that occur in response to a dc current bias are investigated. We present a theoretical model for the nonlinear magnetotransport of graphene carriers. The model is based on the exact solution of the effective Dirac equation in crossed electric and magnetic fields, while the effects of randomly distributed impurities are perturbatively added. To compute the nonlinear current we develop a covariant formulation of the migration center theory. The analysis of the differential resistivity in the large magnetic field region, shows that the extrema of the Shubnikov de Hass oscillations invert when the dc currents exceeds a threshold value. These results are in good agreement with the experimental observations. In the small magnetic field regime, corresponding to large filling factors, the existence of Hall induced resistance oscillations are predicted for ultra clean graphene samples. These oscillations originate from Landau-Zener tunneling between Landau levels, that are tilted by the strong electric Hall field.

Effect of Berry phase on nonlinear response of two-dimensional fermions

“…(30) prevails [25]. We note that a decay of HIROs obtained in earlier numerical calculations of nonlinear resistivity in graphene [26,27] has also been attributed to electron heating, whereas the topological relevance of this effect has been overlooked.…”