Zero-Field Vortex-Induced Hall Effect and Polar Kerr Effect in Chiral p-Wave Superconductors near Kosterlitz-Thouless Transition

Abstract

We discuss Hall effect and power dissipation in chiral p-wave superconductors near Kosterlitz-Thouless transition in the absence of applied magnetic field. In bound pair dynamics picture, nonzero Hall conductivity emerges when vortex-antivortex bound pair polarization has a component transverse to the direction of external perturbation. Such effect arises from the broken time reversal symmetry nature of a chiral p-wave superconducting state and does not require an applied magnetic field. A frequency-dependent matrix dielectric function $\epsilon(\omega)$ is derived to describe the screening effect due to the pair polarization. Quantities related to the Hall conductivity and power dissipation, denoted as $\epsilon^{-1}_\perp$ and $\Im (-\epsilon^{-1}_\parallel)$, are investigated in frequency and temperature domain. The imaginary part of the former can show peak structure and sign reversal as a function of frequency close to transition temperature, as well as in the temperature domain at various fixed frequencies. The latter shows peak structure near transition temperature. These features are attributed to pair-size-dependent longitudinal and transverse response function of bound pairs. Consequences due to free vortex dynamics and the resulting total conductivity tensor $\sigma$ are also discussed.