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SUSY design of smooth quantum rings in graphene

Francisco Correa1, Luis Inzunza1, and Vít Jakubský2

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Phys. Rev. Research 7, 033101 – Published 30 July, 2025

DOI: https://doi.org/10.1103/dtx4-nzby

Abstract

We develop a suitable technique to design zero-energy graphene models with radial electrostatic potentials capable of achieving electrostatic confinement. Using the Gaussian law for electrostatics, we derive the charge density associated with these potentials that correspond to concentric electrostatic rings. The technique is based on a modified supersymmetric transformation that allows us to design time-reversal invariant interaction terms and to find the corresponding zero-energy bound states in analytical form. Consequently, solutions with the same probability density but different angular momentum are characterized by circular probability currents flowing in opposite directions. The energies of the systems defined in two Dirac valleys (one-valley) have a fourfold (twofold) degeneracy. As an example of the technique, we construct a ring-decorated Coulomb potential that exhibits zero-energy collapse and bound states together.

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Phys. Rev. Research 7, 033101– Published 30 July, 2025
  • Received 29 January 2025
  • Accepted 9 June 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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