# The multi-terminal Josephson effect

## TL;DR

This paper reports the first experimental observation of Josephson effects in multi-terminal (3- and 4-terminal) superconducting junctions fabricated from InAs/Al heterostructures, revealing complex supercurrent manifolds and high-order Andreev reflections.

## Contribution

It demonstrates the realization and analysis of multi-terminal Josephson junctions, advancing understanding of their supercurrent manifolds and scattering properties in topological and quantum computing contexts.

## Key findings

- First observation of 3- and 4-terminal Josephson effects.
- Identification of high-order multiple Andreev reflections.
- Supercurrent manifolds sensitive to junction symmetry class.

## Abstract

Establishment of phase-coherence and a non-dissipative (super)current between two weakly coupled superconductors, known as the Josephson effect, plays a foundational role in basic physics and applications to metrology, precision sensing, high-speed digital electronics, and quantum computing. The junction ranges from planar insulating oxides to single atoms, molecules, semiconductor nanowires, and generally to any finite-size coherent conductor. Recently, junctions of more than two superconducting terminals gained broad attention in the context of braiding of Majorana fermions in the solid state for fault-tolerant quantum computing, and accessing physics and topology in dimensions higher than three. Here we report the first observation of Josephson effect in 3- and 4-terminal junctions, fabricated in a top-down fashion from a semiconductor/superconductor (InAs/Al) epitaxial two-dimensional heterostructure. Due to interactions, the critical current of an N-terminal junction becomes the boundary of an (N-1)-dimensional manifold of simultaneously allowed supercurrents. The measured shapes of such manifolds are explained by the scattering theory of mesoscopic superconductivity, and they can be remarkably sensitive to the junction's symmetry class. Furthermore, we observed a notably high-order (up to 8) multiple Andreev reflections simultaneously across every terminals pair, which verifies the multi-terminal nature of normal scattering and a high interface quality in our devices. Given the previously shown gate-control of carrier density and evidence of spin-orbit scattering in InAs/Al heterostructures, and device compatibility with other 2D materials, the multi-terminal Josephson effect reported here can become a testbed for physics and applications of topological superconductivity.