Microscopic theory of nonlinear Hall effect induced by electric field and temperature gradient

We investigate an intriguing phenomenon, the nonlinear chiral thermoelectric (NCTE) Hall effect, where electric current flows parallel to the outer product of an applied electric field and temperature gradient. We develop a general microscopic formulation and confirm the effect in a chiral crystal. Significantly, we find that the contribution of the orbital magnetic moment, which has been previously overlooked, is as crucial as the conventional Berry curvature dipole term. We further demonstrate a substantial NCTE Hall effect in a chiral Weyl semimetal. Our results shed new light on nonlinear transport phenomena and have broad implications for condensed matter physics.