Non-linear responses of strange metals

Understanding the behavior and properties of strange metals remains an outstanding challenge in correlated electron systems. Recently, a model of a quantum critical metal with spatially random couplings [reference Guo, Patel, Esterlis, Sachdev] has been shown to capture the linear in T resistivity down to zero temperature - one of the universal experimental signatures of strange metals. In our work we explore the non-linear transport properties of such a model of strange metal.

Uniting the large-N and Keldysh field theory formalisms we derive a set of kinetic equations for the strange metal and use it to compute nonlinear conductivity.

We find that the third-order conductivity is pronouncedly enhanced in comparison to a Fermi liquid expectation and displays a strong temperature dependence. We attribute this behavior to the strong, non-analytic energy dependence of scattering rate and self-energies for electrons. Additionally, we employ our new formalism to explore the impacts of the external relaxation of the critical boson energy on the fermion dynamics and discuss the bosonic mode drag.