Multi-terminal Josephson junctions as topological materials

TL;DR

This paper proposes that multi-terminal Josephson junctions with conventional superconductors can serve as tunable topological materials in higher dimensions, exhibiting Weyl singularities and quantized transconductance.

Contribution

It introduces a novel approach to realize tunable topological phases using multi-terminal Josephson junctions, extending topological material concepts to higher dimensions.

Findings

Weyl singularities can exist in the Andreev spectrum of n-terminal junctions for n≥4.

Topological transitions manifest as quantized changes in transconductance.

The approach enables tuning topological properties via superconducting phase differences.

Abstract

Topological materials and their unusual transport properties are now at the focus of modern experimental and theoretical research. Their topological properties arise from the bandstructure determined by the atomic composition of a material and as such are difficult to tune and naturally restricted to $\leq3$ dimensions. Here we demonstrate that $n$-terminal Josephson junctions with conventional superconductors may provide a straightforward realization of tunable topological materials in $n-1$ dimensions. For $n\geq 4$, the Andreev subgap spectrum of the junction can accommodate Weyl singularities in the space of the $n-1$ independent superconducting phases, which play the role of bandstructure quasimomenta. The presence of these Weyl singularities enables topological transitions that are manifested experimentally as changes of the quantized transconductance between two voltage-biased leads, the quantization unit being $2e^2/(\pi\hbar)$.