Anomalous topology and synthetic flat band in multi-terminal Josephson Junctions

TL;DR

This paper explores how the topology of Andreev bound states in multi-terminal Josephson junctions is influenced by BdG symmetry and scattering properties, revealing universal behaviors and potential for quantum information storage.

Contribution

It uncovers the impact of BdG symmetry on topological transitions and demonstrates that Andreev band topology depends solely on the scattering matrix, independent of superconductor topology.

Findings

BdG symmetry affects topological gap closings and Chern number changes.

Andreev band topology is determined by the junction's scattering matrix.

Chiral junctions with quantum Hall states support flat, Berry curvature-free bands.

Abstract

Andreev bound states trapped in a multi-terminal Josephson junction (JJ) can be assigned a synthetic band topology owing to their periodic dependence on the Josephson phase bias. We demonstrate that the BdG symmetry adds a twist to this topological character, i.e., gap closing points may or \textit{may not} correspond to change of Chern number, hence extending the standard paradigm for topological bands. We further show that the topology of Andreev bands depends only on the scattering matrix of the junction and is independent of the topological nature of superconductors forming the JJ hence indicating a universal behaviour of multi-terminal JJ. We also show that the chiral junction, supported by quantum Hall state at the junction region, leads to flat Andreev bands (implying absence of DC Josephson effects) that are devoid of Berry curvature ( implying absence of AC Josephson effects). Such electrically inert JJ may be useful for storage of quantum information in future quantum devices.