Anomalous Currents on Closed Surfaces: Extended Proximity, Partial Quantization, and Qubits

TL;DR

This paper investigates how anomalous currents behave on closed surfaces with partial or weak mass terms, revealing extended proximity effects, partial quantization, and potential applications in flux-charge qubits.

Contribution

It provides a detailed analysis of Dirac anomaly effects on closed topologies with partial mass coverage, introducing new insights into surface currents and qubit applications.

Findings

Smoothly decreasing currents with finite mass regions

Oppositely oriented Hall phases are fully quantized

Potential application for flux-charge qubits

Abstract

Motivated by the surface of topological insulators, the Dirac anomaly's discontinuous dependence on sign of the mass, $m/|m|$, is investigated on closed topologies when mass terms are weak or only partially cover the surface. It is found that, unlike the massive Dirac theory on an infinite plane, there is a smoothly decreasing current when the mass region is not infinite; also, a massive finite region fails to exhibit a Hall current edge--exerting an extended proximity effect, which can, however, be uniformly small--and oppositely orientated Hall phases are fully quantized while accompanied by diffuse chiral modes. Examples are computed using Dirac energy eigenstates on a flat torus (genus one topology) and closed cap cylinder (genus zero topology) for various mass-term geometries. Finally, from the resulting the properties of the surface spectra, a potential application for a flux-charge qubit is presented.