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 $mathbf{E}(t)$ 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 ($simomega^{eta}$) 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 $3omega$ inside the spin liquids.

Optical conductivity and surface plasmon modes of U(1) spin liquid states with large spinon Fermi surfaces

In this paper we study the optical properties of $U(1)$ spin liquids with large spinon Fermi surfaces based on a simple formula for the bulk optical conductivity obtained through the Ioffe-Larkin composition rule. We show that the optical conductivity of $U(1)$ spin liquids at energies above the charge gap has a unique feature that distinguishes them from ordinary insulators. In particular we show the existence of a long-life surface plasmon mode propagating along the interface between a linear medium and the spin liquid at frequencies above the charge gap, which can be detected by the widely used Kretschmann-Raether three-layer configuration.