Modern Theory for the Orbital Moment in a Superconductor

TL;DR

This paper develops a modern theoretical framework to calculate the orbital magnetization in chiral p-wave superconductors, addressing previous challenges and applying it to Sr$_2$RuO$_4$ to explain the elusive edge currents.

Contribution

It extends the normal state theory of orbital magnetization to superconductors, enabling calculations for complex states like chiral p-wave superconductors.

Findings

Finite edge current in Sr$_2$RuO$_4$ predicted but below experimental detection

Provides a potential resolution to the controversy over its gap symmetry

Establishes a general method for orbital magnetization in superconductors

Abstract

The chiral p-wave superconducting state is comprised of spin triplet Cooper pairs carrying a finite orbital angular momentum. For the case of a periodic lattice, calculating the net magnetisation arising from this orbital component presents a challenge as the circulation operator $\hat{\bf{r}} \times \hat{\bf{p}}$ is not well defined in the Bloch representation. This difficulty has been overcome in the normal state, for which a modern theory is firmly established. Here, we derive the extension of this normal state approach, generating a theory which is valid for a general superconducting state, and go on to perform model calculations for a chiral p-wave state in Sr$_2$RuO$_4$. The results suggest that the magnitude of the elusive edge current in Sr$_2$RuO$_4$ is finite, but lies below experimental resolution. This provides a possible solution to the long-standing controversy concerning the gap symmetry of the superconducting state in this material.