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

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 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 non-zero 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 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.

17 pages, 11 figures. Final version

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Cited by in corpus (15)

• Single-electron charge transfer into putative Majorana and trivial modes in individual vortices
• Phenomenology of Majorana zero modes in full-shell hybrid nanowires
• Josephson effect and critical currents in trivial and topological full-shell hybrid nanowires
• Absence of Majorana oscillations in finite-length full-shell hybrid nanowires
• Supercurrent transport through 1$e$-periodic full-shell Coulomb islands
• Subgap states in semiconductor-superconductor devices for quantum technologies: Andreev qubits and minimal Majorana chains
• Subgap transport in superconductor--semiconductor hybrid islands: Weak and strong coupling regimes
• InP/GaSb core-shell nanowires: a novel hole-based platform with strong spin-orbit coupling for full-shell hybrid devices
• Flux-periodic oscillations in proximitized core-shell nanowires
• Fluxoid valve effect in full-shell nanowire Josephson junctions
• Caroli-de Gennes-Matricon Analogs in Full-Shell Hybrid Nanowires
• Superconducting bistability in floating Al islands of hybrid Al/InAs nanowires
• Laughlin charge pumping from interplay of chiral Dirac and chiral Majorana modes
• Absence of Quasi-Majorana False Positives in Full-Shell Hybrid Nanowires
• Fluxoid solitons in superconducting tapered tubes and bottlenecks