A Modern Theory for the Orbital Magnetisation in a Superconductor

The chiral p-wave superconducting state is comprised of spin triplet Cooper pairs carrying a finite orbital magnetic moment. Due to its net orbital magnetisation, such a state may sustain a variety of anomalous phenomena, such as the Kerr effect and edge currents. Calculating the orbital magnetisation in a periodic lattice presents a challenge, however, as the circulation operator r x 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 show the extension of this normal state theory to a general superconducting state. We subsequently present model calculations of the magnetisation in the superconducting state of Sr₂RuO₄, which is considered a strong candidate for chiral p-wave pairing. The results suggest that the magnitude of the elusive edge current in Sr₂RuO₄ is below experimental resolution. This provides a possible resolution to the long-standing controversy concerning the theoretical predictions versus the experimental observation of the orbital magnetic moment in Sr₂RuO₄.