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Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
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Anomalous currents on closed surfaces: extended proximity, partial quantization and qubits.

Alexander Selem1

  • 1Department of Physics, University of California, Berkeley, CA 94720, USA. aselem@berkeley.edu

Journal of Physics. Condensed Matter : an Institute of Physics Journal
|December 11, 2012
PubMed
Summary

Investigating the Dirac anomaly on closed surfaces reveals smooth current changes and quantized Hall phases, unlike infinite planes. This research suggests potential applications for flux-charge qubits.

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Area of Science:

  • Condensed Matter Physics
  • Quantum Field Theory
  • Materials Science

Background:

  • Topological insulators exhibit unique surface properties governed by Dirac equations.
  • The Dirac anomaly shows discontinuous behavior related to mass sign (m/|m|) on infinite surfaces.
  • Understanding these anomalies on finite or partially covered surfaces is crucial for device applications.

Purpose of the Study:

  • To investigate the Dirac anomaly's behavior on closed topologies with weak or partial mass terms.
  • To analyze the impact of finite mass regions on surface currents and Hall effects.
  • To explore potential applications of observed phenomena in quantum computing.

Main Methods:

  • Studied Dirac anomaly on closed topologies (flat torus, cap cylinder).
  • Analyzed mass terms that are weak or partially cover the surface.
  • Computed Dirac energy eigenstates and surface spectra for various mass geometries.

Main Results:

  • Discontinuous mass dependence of the Dirac anomaly becomes a smooth current decrease on finite surfaces.
  • Finite massive regions do not exhibit a Hall current edge effect but show a uniformly small proximity effect.
  • Oppositely oriented Hall phases are fully quantized, accompanied by diffuse chiral modes.

Conclusions:

  • The behavior of the Dirac anomaly differs significantly between infinite and closed surfaces.
  • Quantized Hall phases and diffuse chiral modes are key features on these closed topologies.
  • The findings present a potential application for flux-charge qubits based on surface spectral properties.