Synthetic Flat Bands, Hierarchical Topology, and Phase-Fluctuation-Insensitive Quantized Transconductance in Josephson Junctions

TL;DR

This paper explores topological phases in a three-terminal Josephson junction, revealing synthetic flat bands that enable robust, phase-insensitive quantized transconductance and potential for stable Andreev qubits.

Contribution

It uncovers a hierarchy of topological phases, introduces flat bands that suppress Josephson currents, and demonstrates robust quantized transconductance in Josephson junctions.

Findings

Realization of a Chern insulator phase with monopole charges 

Quantized dipolar invariant characterizes subgap Andreev bound states

Robust quantization of transconductance under voltage bias

Abstract

We uncover hierarchy of topological phases within the synthetic Brillouin zone of a three-terminal Josephson junction's (3-TJJ's) Bogoliubov-de Gennes spectrum. We demonstrate that the above-gap continuum realizes a Chern insulator phase with quantized monopole charges (\pm 1), while the subgap Andreev bound states (ABS) are characterized by a quantized dipolar invariant. By breaking time-reversal symmetry at the junction, we induce synthetic flat bands that suppress DC Josephson currents across the entire phase-bias space. Furthermore, under voltage bias, the junction exhibits a robust quantization of the time-averaged transconductance that is reminiscent of a quantized Hall conductance plateau owing to the flat band limit and its dipole phase. As a byproduct, the flat band produces a global "sweet plateau" of phase insensitivity, surpassing localized sweet spots of conventional superconducting qubits and enabling a robust architecture for symmetry-protected Andreev qubits.