Proposed Chiral Texture of the Magnetic Moments of Unit-Cell Loop Currents in the Pseudogap Phase of Cuprate Superconductors

Abstract

We propose a novel chiral order parameter to explain the unusual polar Kerr effect in underdoped cuprates. It is based on the loop-current model by Varma, which is characterized by the in-plane anapole moment N and exhibits the magnetoelectric effect. We propose a helical structure where the vector N (n) in the layer n is twisted by the angle π/2 relative to N (n−1) , thus breaking inversion symmetry. We show that coupling between magnetoelectric terms in the neighboring layers for this structure produces optical gyrotropy, which results in circular dichroism and the polar Kerr effect.PACS numbers: 74.72. Gh, 78.20.Jq, 78.20.Ek Introduction.-The nature of the pseudogap phase in underdoped cuprate superconductors has been a longstanding problem [1]. A series of optical measurements [2-5] revealed gyrotropy in this state. It was observed that the polarizations of incident and reflected light differ by a small angle θ K , called the polar Kerr angle. Initially, these experiments were interpreted as the evidence for spontaneous time-reversal symmetry breaking. Theoretical models [6-9] derived optical gyrotropy from the anomalous Hall effect. In these scenarios, the order parameter is equivalent to an intrinsic magnetic field perpendicular to the layers, which permeates the system and points inward and outward at the opposite surfaces of a crystal. Therefore, the Kerr angle should have opposite signs at the opposite surfaces of the crystal.However, recent reports [10,11] found that the Kerr angle has the same sign at the opposite surfaces of a sample. Therefore, the observed gyrotropy is not consistent with the time-reversal-symmetry breaking due to a magnetic order and should be interpreted as the evidence for natural optical activity due to chiral symmetry breaking [12]. Systems with helical structures, such as cholesteric liquid crystals and some organic molecules, typically exhibit optical gyrotropy and the polar Kerr effect. It is important that the sign of the Kerr angle in this case is the same at the opposite surfaces of the system, in contrast to the gyrotropy produced by a magnetic order (see

Evidence of Chiral Order in the Charge-Ordered Phase of SuperconductingLa1.875Ba0.125Cuo4Single Crystals Using Pol

“…The inconsistencies of the PKE results with "simple" TRSB phenomena found in our measurements, have recently prompted several theoretical studies to explain these anomalous results [19,22,[26][27][28]. In one set of proposals that requires TRSB, the HTSC is argued to posses a "magnetoelectric state," in which the Hamiltonian of the system acquires a term α ij E i H j , where α ij is a rank-2 pseudotensor.…”

“…Such charge ordering may acquire a definite chirality due to structural effects when the crystal is made as was recently shown by Poccia et al [38] for Bi 2 Sr 2 CaCuO 8þx single crystals. At the same time, Pershoguba et al proposed a combination of a loopcurrent magnetoelectric state with gyrotropy [28]. Thus, more experiments as well as theoretical work are needed to fully understand the nature of chirality in this system.…”

Polar Kerr effect from chiral-nematic charge order

“…a gyrotropic order [44][45][46][47] . However, it has been recently pointed out 48,49 that in a system that satisfies the Onsager relations and is in the linear response regime (when the current is proportional to the electric field) time-reversal symmetry breaking is a necessary precondition for the observation of a non-zero Kerr response. It is possible in principle that Kerr effect in the cuprates may be caused by extrinsic time reversal symmetry breaking such as non-equilibrium effects and non-linear response 48 .…”

Necessity of Time-Reversal Symmetry Breaking for the Polar Kerr Effect in Linear Response

“…[13,14], the authors computed the Kerr angle in the long-wavelength limit, where spatial dispersion is treated to first order in the wavevector, and obtained nonzero results. Several researchers [16][17][18][19] recently adopted this idea to interpret Kerr signals from unconventional superconductors.…”