Penetration Depth in Anyon Superconductivity on Torus

Abstract

We present a model for studying the Meissner effect in anyon superconductivity on torus. By obtaining the explicit forms of screening currents for different geometries of external magnetic fields, we calculate the penetration depth and its dependence on relevant parameters. We find a difference between our model and London theory of bulk superconductors. This can be traced back to the two-dimensional character of electric charge carriers that obey anyonic statistics. Our calculations show that for ground state configuration the fractional statistical nature of carriers is washed out of the final results, whereas for excited states the screening currents — and hence the penetration depth — explicitly depend on the fractional phase of the model.