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arXiv · 1201.5708

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

Alexander Selem
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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.

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Alexander Selem. 2012-12-06. Anomalous Currents on Closed Surfaces: Extended Proximity, Partial Quantization, and Qubits. https://doi.org/10.1088/0953-8984%2F25%2F4%2F045003

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