Recent progress on superconductors with time-reversal symmetry breaking.

Superconductivity and magnetism are adversarial states of matter. The presence of spontaneous magnetic fields inside the superconducting state is, therefore, an intriguing phenomenon prompting extensive experimental and theoretical research. In this review, we discuss recent experimental discoveries of unconventional superconductors which spontaneously break time-reversal symmetry and theoretical efforts in understanding their properties.

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.

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.

Spin-orbit coupling and k-dependent Zeeman splitting in strontium ruthenate.

We compare the relativistic LDA Fermi surface of Sr2RuO4 to direct experimental evidence of spin-orbit coupling from de Haas-van Alphen experiments. The k-dependence of the Zeeman splitting at the Fermi surface is modelled with a range of tight binding models of the quasi-particle bands. Only a very restricted class of parameters are consistent with evidence from the de Haas-van Alphen experiments for a strong k-dependent Zeeman splitting on the alpha Fermi surface sheet.

Impurity bound states in disordered d-wave superconductors.

Recent STM experiments on Bi2Sr2Ca2Cu3O10 observed sharp bound states associated with Zn and Ni impurities, as previously predicted theoretically. Here we extend the theory to the case of a finite concentration of impurities. Using the nonlocal coherent potential approximation, we show that the resonance peak both broadens and shifts as a function of impurity concentration.