Microscopic Theory of Nonlinear Hall Effect Induced by Electric Field and Temperature Gradient

Electric current flows parallel to the outer product of an applied electric field and temperature gradient, a phenomenon we call the nonlinear chiral thermo-electric (NCTE) Hall effect. We present a general microscopic formulation of this effect and demonstrate its existence in a chiral crystal. We show that the contribution of the orbital magnetic moment, which has been previously overlooked, is just as significant as the conventional Berry curvature dipole term. Furthermore, we demonstrate a substantial NCTE Hall effect in a chiral Weyl semimetal. These findings offer new insights into nonlinear transport phenomena and have significant implications for the field of condensed matter physics.