Polar Kerr effect from chiral-nematic charge order

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 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 non-zero the mirror symmetries in x and y directions have to be broken, and that for σxy − σyx 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 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 non-zero 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 superconductor, 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.

Interplay between unidirectional and bidirectional charge-density-wave orders in underdoped cuprates

“…In practice, it is more convenient to keep T initially as a parameter and set T = T cdw (x) at a later stage. At the lowest T ≪ v x Λ, the coefficients β i have been obtained previously 15,16 . In this limit…”

“…The presence of the two axial momenta Q x = (Q, 0) and Q y = (0, Q), and, hence, two distinct U(1) components ∆ Qx = ∆ x and ∆ Qy = ∆ y , naturally raises the question whether both are present simultaneously in the CDW state, or only one component orders [15][16][17][18] . If both ∆ x and ∆ y are present, the CDW order is called bi-directional.…”

“…At the mean-field level, C 4 and U (1) symmetries get broken at the same T . Beyond mean-field, the C 4 → C 2 symmetry breaking occurs at a higher T than the breaking of a continuous U(1) symmetry, and this gives rise to a nematic state at intermediate T 's, in which the rotational C 4 symmetry is broken down to C 2 , but the translational U(1) is preserved 15,19 . The CDW order, either uni-directional or bi-directional, may also break Z 2 time-reversal symmetry, if the phases of the CDW orders with the same Q but opposite center of mass momenta are not identical 15,20,21 .…”

“…In this paper we analyze the interplay between CDW order parameters with momenta Q x and Q y within the spin-fluctuation scenario 15,[25][26][27] . In this scenario, axial CDW order with predominantly d-wave form factor emerges in a paramagnetic state due to effective attrac-tive interaction mediated by soft spin fluctuations peaked at or near (π, π), much like spin-mediated d-wave superconductivity.…”

“…The structure of CDW order without PDW has been analyzed before 15,16,20 , but only at its onset and at the lowest T . In this work we extend the analysis of CDW order at the onset to larger T , and also analyze the structure of CDW order inside the ordered phase.…”