Uniaxial strain induced third-order Hall effect in graphene

The transport phenomenon associated with the band geometric quantity has attracted a great deal of attention, and it has gone into the nonlinear terrain. Recently, the Berry connection polarizability has been discovered to be another intrinsic band geometric quantity that contributes to the third-order nonlinear Hall effect, which is prominent in nonmagnetic material with inversion symmetry or a twofold rotation. Based on the first-principles calculations, we find that graphene provides a promising platform for modulating third-order Hall response to applied electric field. By applying the uniaxial strain with breaking the 3-fold rotation symmetry, third-order Hall effect in graphene emerges and is estimated to be observable in experiments. This is attributed to the strain-induced anisotropy and tilt of the energy spectrum. Moreover, the sign of transverse conductivity is opposite for two different strain directions: along the zigzag and armchair directions. Through the strain engineering, our results indicate the possible nonlinear Hall effect in a large number of twodimensional materials with time-reversal symmetry and inversion symmetry.