Circular dichroism and birefringence in unconventional superconductors

We present a theoretical analysis of circular dichroism and birefringe in unconventional BCS superconductors with appropriate broken symmetries. We show that for the effect to exist, that in addition to broken time-reversal and two-dimensional parity symmetries, it is necessary to take into account the weak particle-hole asymmetry of the low-energy excitations of the metallic state. Circular dichroism and birefringence are shown to arise from the order parameter collective mode response of the superconductor; in the clean limit the contribution to the current response from the single-particle excitations does not give rise to circular dichroism or birefringence, even with particle-hole asymmetry. The magnitude of the circular dichroism is found to be small for the classes of superconductors which are thought to be likely candidates to exhibit the requisite broken symmetries, namely the heavy fermions and oxide superconductors. The order of magnitude of the elliptical polarization of a linearly polarized incident wave is V_f/c(ζ/λ_L) (Δ/E_f) ln(E_f/Δ), which is roughly 10^-7-10^-8 rad at frequencies of order the gap, and decreases at least as fast as (2Δ/ω)² at higher frequencies.