Intrinsic optical dichroism in the chiral superconducting state of Sr2RuO4

Quantum-Geometry-Induced Anomalous Hall Effect in Nonunitary Superconductors and Application to Sr_{2}RuO_{4}

The polar Kerr effect and the closely related anomalous charge Hall effect are among the most distinguishing signatures of the superconducting state in Sr_{2}RuO_{4}, as well as in several other compounds. These effects are often thought to be derived from chiral superconducting pairing, and different mechanisms have been invoked for the explanation. However, the intrinsic mechanisms proposed previously often involve unrealistically strong interband Cooper pairing. We show in this Letter that, even without interband pairing, nonunitary superconducting states can support the intrinsic anomalous charge Hall effect, thanks to the quantum geometric properties of the Bloch electrons. The key here is to have a normal-state spin Hall effect, for which a nonzero spin-orbit coupling is essential. A finite charge Hall effect then naturally arises at the onset of a spin-polarized nonunitary superconducting pairing. It depends on both the spin polarization and the normal-state electron Berry curvature, the latter of which is the imaginary part of the quantum geometric tensor of the Bloch states. Applying our results to the weakly paired Sr_{2}RuO_{4} we conclude that, if the reported Kerr effect is of intrinsic origin, the superconducting state is most likely nonunitary and has odd parity. Our theory may be generalized to other superconductors that exhibit the polar Kerr effect.

Effect of nonequilibrium order parameter on the optical response of superconductor Sr2RuO4

The breaking of time reversal symmetry of the superconducting pairings is expected to manifest itself through characteristic transport properties such as a non-zero Kerr angle which provides fingerprint of the quantum anomalous Hall state. In this work, we theoretically study the Kerr effect or the Hall-type response and also consider how this response is modified by the nonequilibrium shape of order parameter of the superconducting state due to the influence of the electromagnetic radiation for the most favorable candidates of chiral superconducting order parameters and of the non-chiral states in strontium ruthenate (Sr₂RuO₄). The unique sensitivity of the Hall-type response introduced above to different types of pairings can be used to identify the most favored pairing which is a serious doubt on the superconducting state of this material.

Time Reversal Symmetry Breaking Superconductors: Sr2RuO4 and Beyond

Recent work done on the time reversal symmetry (TRS) breaking superconductors is reviewed in this paper. The special attention is paid to Sr 2 RuO 4 believed to be spin triplet chiral p-wave superconductor which break TRS and is expected to posses non-trivial topological properties. The family of TRS breaking superconductors is growing relatively fast, with many of its newly discovered members being non-centrosymmetric. However not only Sr 2 RuO 4 but also many other superconductors which possess center of inversion also break TRS. The TRS is often identified by means of the muon spin relaxation ( μ SR) and the Kerr effect. Both methods effectively measure the appearance of the spontaneous bulk magnetic field below superconducting transition temperature. This compound provides an example of the material whose many band, multi-condensate modeling has enjoyed a number of successes, but the full understanding has not been achieved yet. We discuss in some details the properties of the material. Among them is the Kerr effect and by understanding has resulted in the discovery of the novel mechanism of the phenomenon. The mechanism is universal and thus applicable to all systems with multi-orbital character of states at the Fermi energy.

Possible Three-Dimensional Nematic Odd-Parity Superconductivity in Sr_{2}RuO_{4}

The superconducting pairing in Sr_{2}RuO_{4} is widely considered to be chiral p wave with d[over →]_{k}∼(k_{x}+ik_{y})z[over ^], which belongs to the E_{u} representation of the crystalline D_{4h} group. However, this superconducting order appears hard to reconcile with a number of key experiments. In this Letter, based on symmetry analysis we discuss the possibility of odd-parity pairing with inherent three-dimensional character enforced by the interorbital interlayer coupling and the sizable spin-orbit coupling in the material. We focus on a yet unexplored E_{u} pairing, which contains finite (k_{z}x[over ^], k_{z}y[over ^]) component in the gap function. Under appropriate circumstances a novel time-reversal invariant nematic pairing can be realized. This nematic superconducting state could make contact with some puzzling observations on Sr_{2}RuO_{4}, such as the absence of spontaneous edge current and no evidence of split transitions under uniaxial strains.

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.

Odd-Frequency Superconductivity in Sr_{2}RuO_{4} Measured by Kerr Rotation

We establish the existence of bulk odd-frequency superconductivity in Sr_{2}RuO_{4} and show that an intrinsic Kerr effect is direct evidence of this state. We use both general two- and three-orbital models, as well as a realistic tight-binding description of Sr_{2}RuO_{4} to demonstrate that odd-frequency pairing arises due to finite hybridization between different orbitals in the normal state, and is further enhanced by finite interorbital pairing.

Kerr Effect from Diffractive Skew Scattering in Chiral p_{x}±ip_{y} Superconductors

We calculate the temperature dependent anomalous ac Hall conductance σ_{H}(Ω,T) for a two-dimensional chiral p-wave superconductor. This quantity determines the polar Kerr effect, as it was observed in Sr_{2}RuO_{4} [J. Xia et al., Phys. Rev. Lett. 97, 167002 (2006)]. We concentrate on a single band model with an arbitrary isotropic dispersion relation subjected to rare, weak impurities treated in the Born approximation. As we explicitly show by detailed computation, previously omitted contributions to the extrinsic part of an anomalous Hall response, physically originating from diffractive skew scattering on quantum impurity complexes, appear to the leading order in the impurity concentration. By direct comparison with published results from the literature we demonstrate the relevance of our findings for the interpretation of the Kerr effect measurements in superconductors.

Chiral superconductors

Chiral superconductivity is a striking quantum phenomenon in which an unconventional superconductor spontaneously develops an angular momentum and lowers its free energy by eliminating nodes in the gap. It is a topologically non-trivial state and, as such, exhibits distinctive topological modes at surfaces and defects. In this paper we discuss the current theory and experimental results on chiral superconductors, focusing on two of the best-studied systems, Sr2RuO4, which is thought to be a chiral triplet p-wave superconductor, and UPt3, which has two low-temperature superconducting phases (in zero magnetic field), the lower of which is believed to be chiral triplet f-wave. Other systems that may exhibit chiral superconductivity are also discussed. Key signatures of chiral superconductivity are surface currents and chiral Majorana modes, Majorana states in vortex cores, and the possibility of half-flux quantum vortices in the case of triplet pairing. Experimental evidence for chiral superconductivity from μSR, NMR, strain, polar Kerr effect and Josephson tunneling experiments are discussed.

The Berry curvature of the Bogoliubov quasiparticle Bloch states in the unconventional superconductor Sr2RuO4

We will extend the concept of electron band Berry curvatures to superconducting materials. We show that this can be defined for the Bogoliubov-de Gennes equation describing the superconducting state in a periodic crystal. In addition, the concept is exploited to understand the driving mechanism for the optical Kerr effect in time reversal symmetry breaking superconductors. Finally, we establish a sum rule analogue to the normal state Hall sum rule making quantitative contact between the imaginary part of the optical conductivity and the Berry curvature. The general theory will be applied and tested against the drosophila of the p-wave paired materials Sr2RuO4.