Aharonov-Bohm magnetism and Landau diamagnetism in semimetals

TL;DR

This paper analyzes the magnetic responses of semimetals to Aharonov-Bohm flux and uniform magnetic fields, revealing nullified effects, ferromagnetic ground states, and size-dependent diamagnetic susceptibility.

Contribution

It introduces new theoretical predictions on magnetic responses in semimetals, including nullification of Aharonov-Bohm effects and size-dependent diamagnetic susceptibility.

Findings

Nullification of Aharonov-Bohm effect for certain dispersion laws

Ferromagnetic broken symmetry in graphene tubes at zero flux

Logarithmic size dependence of diamagnetic susceptibility

Abstract

We compute the magnetic response of hollow semimetal cylinders and rings to the presence of an axial Aharonov-Bohm magnetic flux, in the absence of interactions. We predict nullification of the Aharonov-Bohm effect for a class of dispersion laws that includes "non-relativistic" dispersion and demonstrate that at zero flux the ground-state of a very short "armchair" graphene tube will exhibit a ferromagnetic broken symmetry. We also compute the diamagnetic response of bulk semimetals to the presence of a uniform magnetic field, specifically predicting that the susceptibility has a logarithmic dependence on the size of the sample.