Relativistic fermion on a ring: Energy spectrum and persistent current

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.

LaTex, 11 pages, 11 figures

References in corpus (7)

• Substrate-induced band gap opening in epitaxial graphene
• Andreev reflection and Klein tunneling in graphene
• Aharonov-Bohm effect and broken valley-degeneracy in graphene rings
• Persistent current in ballistic mesoscopic rings with Rashba spin-orbit coupling
• Large Bandgap Opening Between Graphene Dirac Cones Induced by Na Adsorption onto an Ir Superlattice
• Hermiticity of the Dirac Hamiltonian in Curved Spacetime
• Persistent currents in a graphene ring with armchair edges

Cited by in corpus (5)

• Orbital Magnetization of Quantum Spin Hall Insulator Nanoparticles
• Relativistic persistent currents in ideal Aharonov-Bohm rings
• Relativistic currents on ideal Aharonov-Bohm cylinders
• Aharonov-Bohm rings in de Sitter expanding universe
• Temperature dependent diamagnetic-paramagnetic transitions in metal/semiconductor quantum rings