Intrinsic optical dichroism in the chiral superconducting state of Sr${}_2$RuO${}_4$

We present an analysis of the Hall conductivity ${\sigma }_{xy}(\omega ,T)$ in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is non-zero in systems with inter-band order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity $Im{\sigma }_{xy}(\omega ,T)$, which can be tested experimentally.