Theory of drude-like nonlinear thermoelectric responses in quantum many-body systems

A well-defined Drude peak in the linear electrical response is a fundamental feature of good metals, which has served as a basic probe of quantum materials irrespective of whether correlation is strong or not. We theoretically investigate Drude-like physics in general second-order nonlinear thermoelectric responses in time-reversal invariant noncentrosymmetric quantum many-body systems. The physical interpretations of the corresponding Drude weights are clarified, and the Drude relaxation time is discussed in the framework of the memory matrix technique. In particular, in linear responses the Drude weight is known to be related to the adiabatic derivative of the current with respect to twisted boundary conditions; while in the nonlinear case we find that the Drude weights are related to the adiabatic derivatives of dissipationless linear responses. In addition, we prove a general nonlinear reciprocal relation, and discuss nonlinear generalizations of the Lorentz ratio. Our results generalize the nonlinear Hall effect pointed out by Sodemann and Fu, and hold irrespective of whether quasiparticle descriptions are valid at low energies or not, indicating that nonlinear thermoelectric responses can serve as additional probes of strongly correlated systems such as non-Fermi liquids.