Andreev crystals in hybrid Josephson junction arrays

TL;DR

This paper develops a theoretical model for Andreev crystals in Josephson junction arrays, revealing directional bands that enable tunable, unidirectional signal filtering based on phase bias and interface transparency.

Contribution

It introduces a novel theoretical framework for understanding transport in Andreev crystals, highlighting their directional band properties and potential for unidirectional signal filtering.

Findings

Directional bands form at high interface transparency.

Bands are tunable by flux and bias voltage.

Device can act as a unidirectional filter.

Abstract

Andreev bound states are superpositions of electrons and holes in a metal that form by coherent reflection from a superconductor. When the length of the superconductor is comparable to the superconducting coherence length, Andreev bound states at opposite edges hybridize by quasiparticle tunneling. In a periodic array, these hybridized bound states form a band at energies below the superconducting gap. In this paper, we derive a theoretical framework for the transport properties of these Andreev crystals. We demonstrate that at high interface transparency and constant phase bias between neighboring superconductors, these bands are {\it directional}: one band consists only of right -- while the other only of left-moving electronic states. This property enables the application of this device as a flux- and bias-voltage tunable filter that permits signal transmission in only one direction.