Polar Kerr effect from chiral-nematic charge order

We analyze the polar Kerr effect in an itinerant electron system on a square lattice in the presence of a composite charge order proposed for the pseudogap state in underdoped cuprates. This composite charge order preserves discrete translational symmetries, and is "chiral nematic" in the sense that it breaks time-reversal symmetry, mirror symmetries in x and y directions, and C4 lattice rotation symmetry. The Kerr angle θK in C4-symmetric system is proportional to the antisymmetric component of the anomalous Hall conductivity σxy-σyx. We show that this result holds when C4 symmetry is broken. We show that in order for σxy and σyx to be nonzero the mirror symmetries in x and y directions have to be broken, and that for σxy-σyx to be nonzero time-reversal symmetry has to be broken. The chiral-nematic charge order satisfies all these conditions, such that a nonzero signal in a polar Kerr effect experiment is symmetry allowed. We further show that to get a nonzero θK in a one-band spin-fluctuation scenario, in the absence of disorder, one has to extend the spin-mediated interaction to momenta away from (π,π) and has to include particle-hole asymmetry. Alternatively, in the presence of disorder, one can get a nonzero θK from impurity scattering: either due to skew scattering (with non-Gaussian disorder) or due to particle-hole asymmetry in case of Gaussian disorder. The impurity analysis in our case is similar to that in earlier works on Kerr effect in px+ipy superconductors, however, in our case, the magnitude of θK is enhanced by the flattening of the Fermi surface in the "hot" regions, which mostly contribute to charge order.