Theory of Caroli–de Gennes–Matricon analogs in full-shell hybrid nanowires

Pablo San-Jose, Carlos Payá, C. M. Marcus, S. Vaitiekėnas, and Elsa Prada
Phys. Rev. B 107, 155423 – Published 19 April 2023

Abstract

Full-shell nanowires are hybrid nanostructures consisting of a semiconducting core encapsulated in an epitaxial superconducting shell. When subject to an external magnetic flux, they exhibit the Little-Parks (LP) phenomenon of flux-modulated superconductivity, an effect connected to the physics of Abrikosov vortex lines in type-II superconductors. We show theoretically that full-shell nanowires can host subgap states that are a variant of the Caroli–de Gennes–Matricon (CdGM) states in vortices. These CdGM analogs are shell-induced Van Hove singularities in propagating core subbands. We elucidate their structure, parameter dependence, and behavior in tunneling spectroscopy through a series of models of growing complexity. Using microscopic numerical simulations, we show that CdGM analogs exhibit a characteristic skewness towards higher flux values inside nonzero LP lobes resulting from the interplay of three ingredients. First, the orbital coupling to the field shifts the energy of the CdGM analogs proportionally to the flux and to their generalized angular momentum. Second, CdGM analogs coalesce into degeneracy points at flux values for which their corresponding radial wavefunctions are threaded by an integer multiple of the flux quantum. And third, the average radii of all CdGM-analog wavefunctions inside the core are approximately equal for realistic parameters and are controlled by the electrostatic band bending at the core/shell interface. As the average radius moves away from the interface, the degeneracy points shift towards larger fluxes from the center of the LP lobes, causing the skewness. This analysis provides a transparent interpretation of the nanowire spectrum that allows to extract microscopic information by measuring the number and skewness of CdGM analogs. Moreover, it allows to derive an efficient Hamiltonian of the full-shell nanowire in terms of a modified hollow-core model at the average radius.

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  • Received 23 January 2023
  • Revised 27 March 2023
  • Accepted 29 March 2023

DOI:https://doi.org/10.1103/PhysRevB.107.155423

©2023 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Pablo San-Jose1, Carlos Payá1, C. M. Marcus2, S. Vaitiekėnas2, and Elsa Prada1

  • 1Instituto de Ciencia de Materiales de Madrid, Consejo Superior de Investigaciones Científicas (ICMM-CSIC), E-28049 Madrid, Spain
  • 2Center for Quantum Devices, Niels Bohr Institute, University of Copenhagen, 2100 Copenhagen, Denmark

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Issue

Vol. 107, Iss. 15 — 15 April 2023

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