Polar Kerr effect from chiral-nematic charge order

TL;DR

This paper investigates how a specific chiral-nematic charge order in underdoped cuprates can produce a polar Kerr effect, linking symmetry breaking to observable optical phenomena, and explores mechanisms for non-zero Kerr signals including disorder effects.

Contribution

It demonstrates that chiral-nematic charge order can produce a non-zero polar Kerr effect through symmetry considerations and analyzes how disorder and extended interactions contribute to the effect.

Findings

Kerr angle is proportional to the antisymmetric part of anomalous Hall conductivity.

Breaking mirror symmetries and time-reversal symmetry is necessary for non-zero Kerr effect.

Disorder can induce Kerr effect via skew scattering or particle-hole asymmetry.

Abstract

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 $C_4$ lattice rotation symmetry. The Kerr angle $\theta_K$ in $C_4$-symmetric system is proportional to the antisymmetric component of the anomalous Hall conductivity $\sigma_{xy}-\sigma_{yx}$. We show that this result holds when $C_4$ symmetry is broken. We show that in order for $\sigma_{xy}$ and $\sigma_{yx}$ to be non-zero the mirror symmetries in $x$ and $y$ directions have to be broken, and that for $\sigma_{xy}-\sigma_{yx}$ to be non-zero time-reversal symmetry has to be broken. The chiral-nematic charge order satisfies all these conditions, such that a non-zero signal in a polar Kerr effect experiment is symmetry allowed. We further show that to get a non-zero $\theta_K$ in a one-band spin-fluctuation scenario, in the absence of disorder, one has to extend the spin-mediated interaction to momenta away from $(\pi,\pi)$ and has to include particle-hole asymmetry. Alternatively, in the presence of disorder one can get a non-zero $\theta_K$ 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 $p_x+ip_y$ superconductor, however in our case the magnitude of $\theta_K$ is enhanced by the flattening of the Fermi surface in the "hot" regions which mostly contribute to charge order.