Nonlinear optical conductivity of U(1) spin liquids with large spinon Fermi surfaces

In this paper we study the nonlinear current response of U(1) spin liquids with large spinon Fermi surfaces under the perturbation of a time-dependent ac electric field E(t) within the framework of an effective U(1) gauge theory. In particular, the third-order nonlinear current response to ac electric fields is derived. We show that as in the case of linear current response, an in-gap power-law (∼ωη) response is found for the nonlinear current at low frequency. The nonlinear susceptibility may also induce through process of third harmonic generation propagating EM wave with frequency 3ω inside the spin liquids.