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Directional conductance of Andreev crystals in hybrid Josephson junction arrays

Anders Enevold Dahl1, Andrea Maiani2,3, Max Geier4, Javad Shabani2, and Karsten Flensberg1

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Phys. Rev. B 113, 184513 – Published 11 May, 2026

DOI: https://doi.org/10.1103/zrt6-971d

Abstract

Andreev bound states are coherent electron-hole superpositions that form in a normal metal through repeated Andreev reflection at a superconducting interface. When the length of a superconducting segment is comparable to the coherence length, the bound states on opposite sides of the segment hybridize through quasiparticle tunneling. In a periodic array, these hybridized Andreev bound states form energy bands below the superconducting gap. We develop a theoretical framework for transport in such Andreev crystals. We demonstrate that, at high interface transparency, a constant phase bias between neighboring superconductors renders the bands directional: one band contains only right-moving and the other only left-moving electronic states. This property leads to a directional conductance that enables the device to operate as a flux- and bias-voltage-tunable filter that allows signal transmission in only one direction.

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Phys. Rev. B 113, 184513– Published 11 May, 2026
  • Received 3 September 2025
  • Accepted 27 April 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Funded by Bibsam.

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