Polar Kerr effect from a time-reversal symmetry breaking unidirectional charge density wave

Abstract

We analyze the Hall conductivity σ xy (ω) of a charge ordered state with momentum Q = (0,2Q) and calculate the intrinsic contribution to the Kerr angle K using the fully reconstructed tight-binding band structure for layered cuprates beyond the low energy hot spot model and particle-hole symmetry. We show that such a unidirectional charge density wave (CDW), which breaks time-reversal symmetry, as recently put forward by Wang and Chubukov [Phys. Rev. B 90, 035149 (2014)], leads to a nonzero polar Kerr effect, as observed experimentally. In addition, we model a fluctuating CDW via a large quasiparticle damping of the order of the CDW gap and discuss possible implications for the pseudogap phase. We can qualitatively reproduce previous measurements of underdoped cuprates, but making quantitative connections to experiments is hampered by the sensitivity of the polar Kerr effect with respect to the complex refractive index n(ω). Introduction. One of the most controversial topics in the field of high-temperature superconductivity is the origin of the so-called pseudogap phenomenon observed by various experimental techniques in the underdoped cuprates [1-3] at temperatures T * being larger than the superconducting transition temperature T c . A large number of theoretical scenarios have been initially proposed to explain the origin of the pseudogap [4]. Recent experimental studies of hole-doped cuprates, however, have indicated that the pseudogap region of the high-T c cuprates is a state which competes with superconductivity, and also breaks several symmetries [5][6][7][8][9][10][11][12]. In particular, x-ray and neutron scattering experiments as well as scanning tunneling microscopy (STM) have found the breaking of the lattice symmetry from C 4 down to C 2 below the pseudogap temperature T * in several cuprate compounds [5][6][7]10]. In addition, recent findings of the polar Kerr effect [9,[11][12][13], and the intraunit cell magnetic order [14] point towards breaking of time-reversal or mirror symmetries in the underdoped cuprates. Furthermore, direct indications in favor of the static incommensurate charge-density-wave (CDW) order with momenta Q x = (2Q,0) and/or Q y = (0,2Q) were found by x-ray measurements [15][16][17][18], the nuclear magnetic resonance technique [19][20][21], and in experiments on the sound velocity in a magnetic field [22]. In addition, quantum oscillation measurements indicate a reconstructed band structure with small Fermi surfaces [23][24][25][26]. In these systems 2Q refers to the distance between the so-called hot spots on the Fermi surface, i.e., points where the magnetic Brillouin zones intersect the Fermi surface (FS). It was also argued that the charge order has a predominantly d-wave form factor [10] and that the formation of Fermi surface arcs coincides with the formation of CDW order [27].Possible explanations of the charge order and other related symmetry breaking include loop-current order [28] or ddensity-wave (current) order [29]. Within the so-called spin fluctuation scenario...

Interplay between pair density waves and random field disorders in the pseudogap regime of cuprate superconductors

“…This order parameter is translational invariant (hence giving rise to an IUC order observed in PND), odd under either time reversal symmetry and parity, and invariant under their product. (We note that from a pure CDW order, one can also construct a similar composite TRSB order [95,96]) Since this LC order is originated from the PDW, so its characteristic temperature is the same as T * , which is indeed observed in the PND [27][28][29]. At first sight, in the PDW4 model this order l a is incompatible with the CDW order ρ 2Qa .…”

“…(We note that from a pure CDW order, one can also construct a similar composite TRSB order [95,96]) Since this LC order is originated from the PDW, so its characteristic temperature is the same as T * , which is indeed observed in the PND [27][28][29]. At first sight, in the PDW4 model this order l a is incompatible with the CDW order ρ 2Qa .…”

Calculation for polar Kerr effect in high-temperature cuprate superconductors

“…the pseudogap phase 11,12 if they are accompanied by spontaneous currents [49][50][51][52] . However, the theories [49][50][51][52] are currently formulated for a single layer, and it remains to be seen whether they can be generalized to a multilayer model with alternating sign of σ xy similar to the present work.…”

Emergence of charge order in a staggered loop-current phase of cuprate high-temperature superconductors

“…Experimentally, domains of uniaxial order are seen in Bi 2 Sr 2 CaCu 2 O 8+x , 21 while biaxial order is implied by magneto-oscillation experiments in YBa 2 Cu 3 O 6+x . 7 In our calculations, the biaxial dCDW state is of particular interest because it breaks all mirror symmetries of the lattice, and coupled with the timereversal symmetry breaking of the πLC phase should generate a polar Kerr effect, 89,90…”