Nonlinear Anomalous Thermoelectric Current

Using the concept of the orbital magnetic quadrupole, we derive a nonlinear anomalous thermoelectric current, i.e. a current quadratic in temperature gradient and perpendicular to its direction. In the system that breaks time reversal, inversion, and one mirror symmetry, but has the combined time reversal and inversion symmetry, the linear anomalous thermoelectric current vanishes but the nonlinear current we obtained does not vanish and hence can be used to probe such system. We demonstrate this nonlinear current in the loop-current model in the pseudogap phase.