Electron-hole coherence in core-shell nanowires with partial proximity induced superconductivity

TL;DR

This study numerically investigates electron-hole coherence in core-shell nanowires with partial superconductivity, revealing how different proximitization geometries influence superconducting properties and Andreev reflection phenomena.

Contribution

It introduces a detailed numerical analysis of partial proximity effects in nanowires, exploring radial, angular, and longitudinal cases and their impact on coherence and superconductivity.

Findings

Radial proximitization causes localization maxima at the shell center.

Superconductivity gap depends on the proximitized shell thickness ratio.

Angular and longitudinal cases show signatures of Andreev reflection.

Abstract

By solving the Bogoliubov-de Gennes Hamiltonian, the electron-hole coherence within a partially proximitized n-doped semiconductor shell of a core-shell nanowire heterostructure is investigated numerically and compared with the Andreev reflection interpretation of proximity induced superconductivity. Partial proximitization is considered to quantify the effects of a reduced coherence length. Three cases of partial proximitization of the shell are explored: radial, angular and longitudinal. For the radial case, it is found that the boundary conditions impose localization probability maxima in the center of the shell in spite of off-center radial proximitization. The induced superconductivity gap is calculated as a function of the ratio between the proximitized shell thickness and the total shell thickness. In the angular case, the lowest energy state of a hexagonal wire with a single proximitized side is found to display the essence of Andreev reflection, only by lengthwise summation of the localization probability. In the longitudinal case, a clear correspondence with Andreev reflection is seen in the localization probability as a function of length along a half-proximitized wire. The effect of an external magnetic field oriented along the wire is explored.