Zero-Field Vortex-Induced Hall Effect and Polar Kerr Effect in Chiral p-Wave Superconductors near Kosterlitz-Thouless Transition
In this work, we investigate polar Kerr effect and Ohmic conductivity induced by vortex dynamics in a chiral p-wave superconducting thin film near Kosterlitz-Thouless (KT) transition without explicitly applying magnetic field. Due to the broken time reversal symmetry in the superconducting state and the breaking of Galilean invariance by forces originated from impurities, a conductivity tensor with nonzero off-diagonal element is expected. We generalize the dynamical theory developed by Ambegaokar, Halperin, Nelson, and Siggia to obtain a matrix dielectric function describing vortex screening, which is further related to the conductivity tensor. Polar Kerr effect due to the nonzero Hall conductivity is studied. The corresponding Kerr angle is shown to be proportional to the imaginary part of off-diagonal component of the dielectric function in certain parameter regime. While the frequency and temperature dependence of dissipation in chiral p-wave context behave similarly to those of s-wave results, the Kerr angle exhibits some novel features near the KT transition. As a result, Kerr angle measurement in experiment can provide a probe of vortex dynamics described in this work.