Anomalous Hall conductivity of clean Sr2RuO4 at finite temperatures

Building on previous work, we calculate the temperature- and frequency-dependent {\it anomalous} Hall conductivity for the putative multiband chiral superconductor \Sr using a simple microscopic two-orbital model without impurities. A Hall effect arises in this system without the application of an external magnetic field due to the time-reversal-symmetry breaking chiral superconducting state. The anomalous Hall conductivity is nonzero only when there is more than one superconducting order parameter, involving inter- as well as intra-band Cooper pairing. We find that such a multiband superconducting state gives rise to a distinctive resonance in the frequency-dependence of the Hall conductivity at a frequency close to the inter-orbital hopping energy scale that describes hopping between Ru $d_{xz}$ and $d_{yz}$ orbitals. The detection of this feature, robust to temperature and impurity effects in the superconducting phase, would thus constitute compelling evidence in favour of a multiband origin of superconductivity in \Sr, with strong superconductivity on the $\alpha$ and $\beta$ bands. The temperature dependence of the Hall conductivity and Kerr rotation angle are studied within this model at the one-loop approximation.Comment: 14 pages, 8 figures. Invited submission, proceedings of M2S 2012. Published versio

Impurity scattering and localization in dd-wave superconductors

Strong evidence is presented for the localization of low energy quasiparticle states in disordered $d$-wave superconductors. Within the framework of the Bogoliubov-de Gennes (BdG) theory applied to the extended Hubbard model with a finite concentration of non-magnetic impurities, we carry out a fully self-consistent numerical diagonalization of the BdG equations on finite clusters containing up to $50\times 50$ sites. Localized states are identified by probing their sensitivity to the boundary conditions and by analyzing the finite size dependence of inverse participation ratios.Comment: 4 pages REVTeX with 2 embedded .ps figures; submitted to PRB as Rapid Communicatio

Suppression of Spontaneous Supercurrents in a Chiral p-Wave Superconductor

The superconducting state of SRO is widely believed to have chiral p-wave order that breaks time reversal symmetry. Such a state is expected to have a spontaneous magnetization, both at sample edges and at domain walls between regions of different chirality. Indeed, muon spin resonance experiments are interpreted as evidence of spontaneous magnetization due to domain walls or defects in the bulk. However, recent magnetic microscopy experiments place upper limits on the magentic fields at the sample edge and surface which are as much as two orders of magnitude smaller than the fields predicted theoretically for a somewhat idealized chiral p-wave superconductor. We investigate the effects on the spontaneous supercurrents and magnetization of rough and pair breaking surfaces for a range of parameters within a Ginzburg-Landau formalism. The effects of competing orders nucleated at the surface are also considered. We find the conditions under which the edge currents are significantly reduced while leaving the bulk domain wall currents intact, are quite limited. The implications for interpreting the existing body of experimental results on superconducting SRO within a chiral p-wave model are discussed.Comment: Changes to section 3, typos remove