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 $C_4$ 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 $p_x+i{p}_y$ 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.

16 pages, 6 figures, replaced with published version

References in corpus (24)

• High Resolution Polar Kerr Effect Measurements of Sr2RuO4: Evidence for Broken Time Reversal Symmetry in the Superconducting State
• Quantum phase transitions of metals in two spatial dimensions: II. Spin density wave order
• Polar Kerr Effect Measurements of YBa2Cu3O6+x: Evidence for Broken Symmetry Near the Pseudogap Temperature
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions (Supporting Material)
• From a single-band metal to a high-temperature superconductor via two thermal phase transitions
• Distinct Charge Orders in the Planes and Chains of Ortho-III-Ordered YBa${}_2$Cu${}_3$O${}_{6+\delta }$ Superconductors Identified by Resonant Elastic X-ray Scattering
• Observation of broken time-reversal symmetry in the heavy fermion superconductor UPt${}_3$
• Direct phase-sensitive identification of a d-form factor density wave in underdoped cuprates
• Spin dynamics in the pseudogap state of a high-temperature superconductor
• Evidence for unusual superconducting correlations coexisting with stripe order in La(1.875)Ba(0.125)CuO(4)
• Dichroic f-sum rule and the orbital magnetization of crystals
• Collective modes and electromagnetic response of a chiral superconductor
• Modified Sagnac interferometer for high-sensitivity magneto-optic measurements atcryogenic temperatures
• Frequency and temperature dependence of the anomalous Hall conductivity in a chiral px+ipy superconductor with impurities
• Kerr effect as evidence of gyrotropic order in the cuprates
• Impurity Induced Polar Kerr Effect in A Chiral p-wave Superconductor
• Berry phase mechanism for optical gyrotropy in stripe-ordered cuprates
• Gauge-invariant electromagnetic response of a chiral px+ipy superconductor
• Quantum critical point for stripe order: An organizing principle of cuprate superconductivity
• Composite charge order in the pseudogap region of the cuprates
• Crisscrossed stripe order from interlayer tunneling in hole-doped cuprates
• Theory of the high-frequency chiral optical response in a p_x+ip_y superconductor
• Sr_2 Ru O_4 : Broken Time-Reversal Symmetry in the Superconducting state
• Absence of the polar Kerr effect in the helical loop-current model [Phys. Rev. Lett. 111, 047005 (2013)]

Cited by in corpus (6)

• Coexistence of charge-density-wave and pair-density-wave orders in underdoped cuprates
• Quantum Oscillations in Hole-Doped Cuprates
• Interplay between pair-density-wave and charge-density-wave orders in underdoped cuprates
• Kerr effect from diffractive skew scattering in chiral $p_x\pm i{p}_y$ superconductors
• The Effect of Pointlike Impurities on d_{x^2-y^2} Charge Density Waves in Cuprate Superconductors
• Polar Kerr effect from a time-reversal symmetry breaking unidirectional charge density wave