Relativistic fermion on a ring: Energy spectrum and persistent current

TL;DR

This paper investigates the energy and persistent current spectra of a relativistic fermion on a ring, revealing nonlinear behaviors, critical mass effects, and paramagnetic-diamagnetic transitions, with proposed experimental verification.

Contribution

It provides a detailed analysis of relativistic fermion behavior on a ring, highlighting mass and radius effects on persistent current and susceptibility, and introduces a potential experimental test.

Findings

Existence of a critical mass where current is flux-independent.

Periodic plateaus in current spectrum at lower masses.

Transition from diamagnetic to paramagnetic behavior with decreasing mass or radius.

Abstract

The energy and persistent current spectra for a relativistic fermion on a ring is studied in details. The nonlinear nature of persistent current in relativistic regime and its dependence on particle mass and ring radius are analysed thoroughly. For a particular ring radius we find the existence of a critical mass at which the single ring current doesn't depend on the flux. In lower mass regime the total current spectrum shows plateaus at different height which appears periodically. The susceptibility as well shows periodic nature with amplitude depending on particle mass. As we move from higher mass to lower mass regime, we find that the system turns into paramagnetic from diamagnetic. We also show that same behaviour is observed if one vary the radius of the ring for a fixed particle mass. Hence the larger ring will be diamagnetic while the smaller one will be paramagnetic. Finally we propose an experiment to verify our findings.