Relativistic persistent currents in ideal Aharonov-Bohm rings

Abstract

The exact solutions of the complete Dirac equation for fermions moving in ideal Aharonov-Bohm rings are used for deriving the exact expressions of the relativistic partial currents. It is show that as in the non-relativistic case these currents can be related to the derivative of the fermion energy with respect to the flux parameter. A specific relativistic effect is the saturation of the partial currents for high values of the total angular momentum. Based on this property, the total relativistic persistent current at $T=0$ is evaluated giving its analytical expression and showing how this depend on the ring parameters.