Quantum kinetic theory of nonlinear thermal current

We investigate the second-order nonlinear electronic thermal transport induced by temperature gradient. We develop the quantum kinetic theory framework to describe thermal transport in presence of a temperature gradient. Using this, we predict an intrinsic scattering time independent nonlinear thermal current in addition to the known extrinsic nonlinear Drude and Berry curvature dipole contributions. We show that the intrinsic thermal current is determined by the band geometric quantities and is non-zero only in systems where both the space inversion and time-reversal symmetries are broken. We employ the developed theory to study the thermal response in tilted massive Dirac systems. We show that besides the different scattering time dependence, the various current contributions have distinct temperature dependence in the low temperature limit. Our systematic and comprehensive theory for nonlinear thermal transport paves the way for future theoretical and experimental studies on intrinsic thermal responses.