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Czechoslovak Journal of Physics

Exact results for the persistent current in an aharonov-bohm ring with a quantum impurity

Johan Nilsson, Hans-Peter Eckle, Henrik Johannesson

Published Oct 1, 2006• 1 citation
Publisher
DOI
10.1007/s10582-006-0433-7

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Abstract In this report we revisit the results obtained in [1, 2] where the relativistic Aharonov-Bohm was studied for the first time. The method is based on the exact solutions of the complete (1+3)-dimensional Dirac equation of fermions moving in ideal Aharonov-Bohm (AB) rings and cylinders which are used for deriving the exact expressions of the relativistic partial currents. It is shown that these currents can be related to the derivative of the fermion energy with respect to the flux parameter, just as in the non-relativistic case. However, a new and remarkable 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 currents atT= 0 is evaluated for rings and cylinders obtaining approximative simple closed formulas. Notice that this report brings together the texts of Refs. [1, 2] with some improvements and unitary notations.