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

In recent years, nonlinear transport phenomena, such as nonreciprocal propagation and nonlinear Hall effects, have garnered attention. One fascinating aspect is that they can arise from symmetries different from those governing linear transport phenomena. For example, the nonlinear Hall effect does not necessarily require time-reversal symmetry breaking, indicating that it is fundamentally a different physical phenomenon from linear responses.

In this study, we focus on the nonlinear Hall effect, where a current flows in the direction of the cross product of an electric field and a temperature gradient (referred to here as the nonlinear chiral thermo-electric (NCTE) Hall effect). First, we microscopically formulate the NCTE Hall effect using the nonequilibrium (Keldysh) Green’s function method. By expressing the formula in terms of Green’s functions and then transforming them into a band representation, we compare them with equations derived from the Boltzmann equation and demonstrate the importance of the contribution of the orbital magnetic moment. Additionally, we show that the NCTE Hall effect can indeed be obtained in specific models.