Time-Reversal Symmetry Breaking by a (d+id) Density-Wave State in Underdoped Cuprate Superconductors

Abstract

It was proposed that the id x 2 −y 2 density-wave state (DDW) may be responsible for the pseudogap behavior in the underdoped cuprates. Here we show that the admixture of a small dxy component to the DDW state breaks the symmetry between the counter-propagating orbital currents of the DDW state and, thus, violates the macroscopic time-reversal symmetry. This symmetry breaking results in a non-zero polar Kerr effect, which has recently been observed in the pseudogap phase. 74.25.Nf, 71.27.+a Introduction. The nature of the pseudogap in the cuprate high-temperature superconductors is a much-debated and still unresolved issue [1]. Many of the anomalous properties associated with the pseudogap can be best described as resulting from the order parameters [2], such as those of various density-wave states, competing with the d-wave superconductivity. If a density-wave state were to have an energy gap of the d-wave symmetry on the Fermi surface, in conformity with the pseudogap, the natural candidate would be the id x 2 −y 2 density wave (DDW) state. Indeed, much of the phenomenology of the cuprates in the underdoped regime can be unified [3,4,5] by making a single assumption that the ordered DDW state is responsible for the pseudogap. However, the situation is still controversial, because there is no convincing direct experimental evidence for a phase transition to another state in the underdoped regime, besides the antiferromagnetic order close to half-filling.

Stability of nodal quasiparticles in underdopedYBa2Cu3O6+yprobed by penetration depth and microwave spectroscopy

“…µSR 50 and polar Kerr effect 51 have established the onset of time-reversal-symmetry breaking (TRSB) at T * (p) in YBa 2 Cu 3 O 6+y , but the signals are extremely weak. It has been suggested that a variant of the DDW, the d xy + id x 2 −y 2 density wave, 52 would contain a subdominant but macroscopic TRSB component and be consistent with the small magnitude of the observed effects. Spin-polarized neutron scattering on YBa 2 Cu 3 O 6+y has detected weak signatures of a novel magnetic order that preserves translational symmetry, 53 and has a form consistent with the Θ II circulating current phase proposed by Varma,48 shown in schematic form in the inset of This paper is organized as follows.…”

Frequency and temperature dependence of the anomalous ac Hall conductivity in a chiralpx+ipysuperconductor with impurities

“…A model of this kind, involving formation of the d xy + id x 2 −y 2 density wave, was proposed in Ref. [78] to explain the Kerr effect in underdoped cuprates [2]. The anomalous Hall effect was studied for this model earlier in Ref.…”

“…For non-superconducting systems, the current operator can be expressed in terms of the derivatives ∂Ĥ/∂p of the HamiltonianĤ with respect to the electron quasimomenta p. For a topologically non-trivial band structure, the off-diagonal matrix elements of the current operator between different bands produce a non-zero Berry curvature, and the anomalous Hall conductivity can be expressed completely in terms of the Berry curvature [46,47,[77][78][79][80].…”

Calculation for polar Kerr effect in high-temperature cuprate superconductors

“…Here we show that the observations in high-T c can be understood in the framework of a chiral d-density wave state 30 in the presence of interlayer tunneling, which is invariant under TRS in the bulk, but can still have a non zero PKE because it is a property of the light reflected from the top surface which breaks TRS locally. Therefore PKE in this mechanism would be insensitive to the changing skin depth of the incom- ing light at the top surface, while PKE from a bulk order parameter based description would yield a stronger effect for a longer skin depth.…”