Theory of the Orbital Moment in a Superconductor

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 ˆ r × ˆ 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 Sr2RuO4. The results suggest that the magnitude of the elusive edge current in Sr2RuO4 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.