Theory of dichroism in high-temperature superconductors

Superconductivity in Empty Bands and Multiple Order Parameter Chirality

Recent experiments have shown rotation of the plane of polarization of light reflected from the surface of some superconductors. The photon energy exceeds the electronic bandwidth, so that completely filled or completely empty bands must play a role. We show that in strong-coupling theory a Coulomb interaction can produce an order parameter in the unoccupied band that explains the observations. Thus the phenomenology puts tight constraints on the form of the order parameter in different bands. We propose that the experiments have detected, for the first time, the existence of a superconducting order parameter in a band far from the Fermi energy. This is only possible because of the sensitivity to delicate symmetries: a positive Kerr effect indicates that time reversal and certain mirror symmetries are broken in the ordered phase. Furthermore, detailed analysis of the results implies that in UPt₃ there exist bands that have different order parameter chiralities, opening up complex new possibilities for topological superconductivity.

Intrinsic optical dichroism in the chiral superconducting state of Sr2RuO4

We present an analysis of the Hall conductivity σ(xy)(ω,T) in time reversal symmetry breaking states of exotic superconductors. We find that the dichroic signal is nonzero in systems with interband order parameters. This new intrinsic mechanism may explain the Kerr effect observed in strontium ruthenate and possibly other superconductors. We predict coherence factor effects in the temperature dependence of the imaginary part of the ac Hall conductivity Imσ(xy)(ω,T), which can be tested experimentally.

Is Sr(2)RuO(4) a chiral p-wave superconductor?

Much excitement surrounds the possibility that strontium ruthenate exhibits chiral p-wave superconducting order. Such order would be a solid state analogue of the A phase of He-3, with the potential for leading to exotic physics relevant to quantum computing. We take a critical look at the evidence for such time reversal symmetry breaking order. The possible superconducting order parameter symmetries and the evidence for and against chiral p-wave order are reviewed, with an emphasis on the most recent theoretical predictions and experimental observations. In particular, attempts to reconcile experimental observations and theoretical predictions for the spontaneous supercurrents expected at sample edges and domain walls of a chiral p-wave superconductor and for the polar Kerr effect, a key signature of broken time reversal symmetry, are discussed.

Hall conductivity of a spin-triplet superconductor

We calculate the Hall conductivity for a spin-triplet superconductor, using a generalized pairing symmetry dependent on an arbitrary phase phi. A promising candidate for such an order parameter is Sr2RuO4, whose superconducting order parameter symmetry is still subject to investigation. The value of this phase can be determined through Kerr rotation and dc Hall conductivity measurements. Our calculations impose significant constraints on phi.

Theory of the high-frequency chiral optical response of a p(x) + ip(y) superconductor

The optical Hall conductivity and the polar Kerr angle are calculated as functions of temperature for a two-dimensional chiral p(x) + ip(y) superconductor, where the time-reversal symmetry is spontaneously broken. The theoretical estimate for the polar Kerr angle agrees by the order of magnitude with the recent experimental measurement in Sr2RuO4 by Xia et al. [Phys. Rev. Lett. 97, 167002 (2006)10.1103/PhysRevLett.97.167002]. The theory predicts that the Kerr angle is proportional to the square of the superconducting energy gap and is inversely proportional to the cube of frequency, which can be verified experimentally.