Metamorphosis and Taxonomy of Andreev Bound States

TL;DR

This paper investigates the detailed behavior of Andreev bound states in a superconductor-normal-superconductor junction, revealing complex phenomena like the metamorphosis of normal bound states into Andreev states through numerical analysis.

Contribution

It provides a comprehensive numerical study of Andreev bound states, uncovering phenomena beyond existing analytical approximations in a one-dimensional SNS junction model.

Findings

Confirmation of predicted physics by analytical models

Discovery of the metamorphosis of normal bound states into Andreev states

Rich set of phenomena beyond analytical approximations

Abstract

We analyze the spatial and energy dependence of the local density of states in a SNS junction. We model our system as a one-dimensional tight-binding chain which we solve exactly by numerical diagonalization. We calculate the dependence of the Andreev bound states on position, phase difference, gate voltage, and coupling with the superconducting leads. Our results confirm the physics predicted by certain analytical approximations, but reveal a much richer set of phenomena beyond the grasp of these approximations, such as the metamorphosis of the discrete states of the normal link (the normal bound states) into Andreev bound states as the leads become superconducting.