Relativistic persistent currents in ideal Aharonov-Bohm rings
Ion I. Cotaescu, Doru-Marcel Baltateanu, Ion Cotaescu Jr
TL;DR
This paper derives exact relativistic solutions for fermions in Aharonov-Bohm rings, revealing how relativistic effects influence persistent currents, including current saturation at high angular momentum, and provides analytical expressions for these currents.
Contribution
It presents the first exact relativistic solutions for fermions in Aharonov-Bohm rings and analyzes the impact of relativistic effects on persistent currents.
Findings
Relativistic partial currents relate to the derivative of energy with respect to flux.
Currents saturate at high angular momentum values.
Analytical expression for total persistent current at zero temperature.
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 is evaluated giving its analytical expression and showing how this depend on the ring parameters.
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