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. We discuss the main experimental probes and give an extensive account of theoretical approaches to understand the order parameter symmetries and the corresponding pairing mechanisms, including the importance of multiple bands.

Self-assembly of graphene ribbons by spontaneous self-tearing and peeling from a substrate.

Graphene and related two-dimensional materials have shown unusual and exceptional mechanical properties, with similarities to origami-like paper folding and kirigami-like cutting demonstrated. For paper analogues, a critical difference between macroscopic sheets and a two-dimensional solid is the molecular scale of the thin dimension of the latter, allowing the thermal activation of considerable out-of-plane motion. So far thermal activity has been shown to produce local wrinkles in a free graphene sheet that help in theoretically understanding its stability, for example, and give rise to unexpected long-range bending stiffness. Here we show that thermal activation can have a more marked effect on the behaviour of two-dimensional solids, leading to spontaneous and self-driven sliding, tearing and peeling from a substrate on scales approaching the macroscopic. We demonstrate that scalable nanoimprint-style contact techniques can nucleate and direct the parallel self-assembly of graphene ribbons of controlled shape in ambient conditions. We interpret our observations through a simple fracture-mechanics model that shows how thermodynamic forces drive the formation of the graphene-graphene interface in lieu of substrate contact with sufficient strength to peel and tear multilayer graphene sheets. Our results show how weak physical surface forces can be harnessed and focused by simple folded configurations of graphene to tear the strongest covalent bond. This effect may hold promise for the patterning and mechanical actuating of devices based on two-dimensional materials.

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.

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.

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. The bare LDA bands do not lead to such a strong k-dependent Zeeman splitting on this sheet, and this suggests that additional charge transfer takes place as suggested by DMFT calculations. We conclude that the overall scale of the spin-orbit coupling must be at least as large as the several hundred kelvin deduced in previous work, and that this must call into question any theory postulating rotation of the triplet d-vector at small magnetic fields.

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.