Abstract

We discuss the polar Kerr effect in a chiral $p$-wave (${p}_{x}+i{p}_{y}$-wave) superconductor. It is found that the off-diagonal component of a current-current correlation function is induced by impurity scattering in the chiral $p$-wave condensate, and a nonzero Hall conductivity is obtained using the Kubo formula. We estimate the Kerr rotation angle by using this impurity-induced Hall conductivity and compare it with experimental results [J. Xia et al., Phys. Rev. Lett. 97, 167002 (2006)].

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