Aharonov–Bohm magnetism and Landau diamagnetism in semimetals

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.