Aharonov-Bohm magnetism and Landau diamagnetism in semimetals

TL;DR

The paper develops a unified analytic framework based on spectral zeta-function regularization to study magnetic responses in semimetals, covering Aharonov-Bohm diamagnetism on cylindrical and ring geometries and Landau diamagnetism in bulk systems. By treating the AB problem across general dispersion laws and exploiting analytic continuation, it demonstrates AB nullification for parabolic and other even-power dispersions, predicts a ferromagnetic broken-symmetry ground state in short armchair graphene tubes at zero flux, and reveals a logarithmic dependence of bulk diamagnetic susceptibility on system size. The approach yields explicit expressions for AB energies, moments, and susceptibilities in both cylinder and ring cases and connects the AB and Landau problems through a shared zeta-function formalism, providing a robust tool for finite-size and geometry-dependent magnetism in semimetals. The results illuminate how dispersion, geometry, and boundary conditions govern quantum magnetic responses, with implications for nanoscale graphene-based devices and the interpretation of diamagnetic behavior in semimetallic materials.

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.