Superconductivity in strongly spin-orbit coupled systems

Abstract

Superconductivity is a low-temperature quantum state of matter, marked by the vanishing of electrical resistance and the expulsion of magnetic flux fields. A thorough microscopic understand of superconductivity was gained through the seminal theory by Bardeen, Cooper, and Schrieffer (BCS theory), in which electrons are bound into so-called Cooper pairs by an attractive interaction in the material. In this theory the origin of the attractive interaction is the coupling of electrons to lattice vibrations which makes electrons pair together in a relative orbital s-wave state.

In the last decades, superconductors with properties that cannot be explained by the predictions of BCS theory have been discovered. The pairing mechanism in these unconventional superconductors remains incompletely understood, however, a symmetry-based phenomenological approach has proved to be very useful in determining the stable superconducting states and gap structures even if the pairing mechanism is unknown. More recently, materials with strong spin-orbit coupling have moved into the focus of attention due to their possible unconventional superconductivity. The mixing of orbital and spin degrees of freedom imposes strong constraints on the permissible Cooper pair structures but can be favourable for interesting exotic phenomena.

In this thesis we will theoretically study the physics of superconductors with strong spin-orbit coupling. Using field theory techniques and group theory arguments we investigate the properties of orbitally non-trivial pairing states. The presence of multiple bands qualitatively changes the nodal structure of an inversion-symmetric time-reversal symmetry-breaking superconductor. Instead of point or line nodes, the gap exhibits extended nodal pockets, called Bogoliubov Fermi surfaces.

These surfaces originate from the “inflation” of point and line nodes in the absence of time-reversal symmetry. We present a comprehensive theory for Bogoliubov Fermi surfaces and investigate their thermodynamic stability in a paradigmatic model. We find that a pairing state with Bogoliubov Fermi surfaces can be stabilized at moderate spin-orbit coupling strengths. Our results show that Bogoliubov Fermi surfaces of experimentally relevant size can be thermodynamically stable.

Strontium ruthenate (Sr2RuO4) has long been thought to be the textbook example of an odd-parity spin-triplet chiral p-wave superconducting state. However, recent spin-susceptibility measurements have observed a singlet-like response and cast serious doubts on this prediction. We propose an alternative even-parity pairing state, which is consistent with the new experimental observations. This state can be energetically stable once a realistic three-dimensional model of Sr2RuO4 is considered. This state naturally gives rise to Bogoliubov Fermi surfaces.