1206.2170 (Sumit Ghosh)

Relativistic fermion on a ring: Energy spectrum and persistent current    [PDF]

Sumit Ghosh

We have studied the energy and persistent current spectrum of a relativistic fermion on a one dimensional ring in presence of a Aharonov-Bohm flux. For a particular radius of the ring, we find the existence of a critical value of mass at which the current becomes constant with respect to the flux. This constant value is same as the current produced by a massless particle with same charge. It behaves as a lower cutoff for current as we further decrease the mass. We give a brief description for the case of a massless particle which can be a possible scenario in a graphene ring or on the surface of a topological insulator. We calculated the total current for a large number of isolated rings and find the existence of periodic plateaus in the current-flux curve for lower mass. The width of the plateaus decrease with decrease of mass and they appear as sharp pulses localised at integral flux values as we approach zero mass limit. Finally we propose two experiments to verify our result.

View original: http://arxiv.org/abs/1206.2170