Overlapping Andreev states in semiconducting nanowires: competition of 1D and 3D propagation

TL;DR

This paper investigates overlapping Andreev bound states in a semiconducting nanowire with three superconducting leads, analyzing how 1D and 3D electron propagation regimes compete and influence the ABS spectrum.

Contribution

It introduces a model for ABS in nanowires with overlapping 1D and 3D propagation, detailing spectral transitions and interference effects, including a perturbation theory for hybridization regimes.

Findings

Transition from single to multiple ABS with changing junction separation

Identification of regimes where 1D and 3D overlaps dominate or compete

Analytical perturbation theory for hybridization and interference effects

Abstract

The recent proposals of devices with overlapping Andreev bound states (ABS) open up the opportunities to control and fine-tune their spectrum, that can be used in various applications. In this Article, we study the ABS in a device consisting of a semiconducting nanowire covered with three superconducting leads. The ABS are formed at two junctions where the wire is not covered. They overlap in the wire where the electron propagation is 1D, and in one of the leads where the propagation is 3D. We identify a number of regimes where these two overlaps either dominate or compete, depending on the junction separation $L$ as compared to the correlation lengths $\xi_{\rm w}$, $\xi_{\rm s}$ in the wire and in the lead, respectively. We utilize a simple model of 1D electron spectrum in the nanowire and take into account the quality of the contact between the nanowire and the superconducting lead. We present the spectra for different $L$, detailing the transition from a single-ABS in the regime of strong 1D hybridization to two almost independent ABS hybridized at the degeneracy points, in the regime of weak 1D hybridization. We present the details of merging the upper ABS with the continuous spectrum upon decreasing $L$. We study in detail the effect of quantum interference due to the phase accumulated during the electron passage between the junctions. We develop a perturbation theory for analytical treatment of hybridization. We address an interesting separate case of fully transparent junctions. We derive and exemplify a perturbation theory suitable for the competition regime demonstrating the interference of 1D and two 3D transmission amplitudes.