Topological transconductance quantization in a four-terminal Josephson junction

Abstract

The investigation of topological transitions in quantum systems is a thriving area of modern research. The authors recently predicted that multiterminal Josephson junctions realize a novel type of topological matter. Weyl singularities may appear in the Andreev bound-state spectrum of junctions with four superconducting terminals, giving rise to topological transitions as the superconducting phases are tuned. These transitions manifest themselves in a quantization of the transconductance between two voltage-biased terminals in fundamental units of 4${e}^{2}$2/$h$, where $e$ is the electric charge and $h$ is the Planck constant. The present work addresses the observability of this effect. The quantized transconductance is associated with adiabatic transport at fixed occupations of the Andreev states. On the other hand, a bias voltage leads to multiple Andreev reflections, where a quasiparticle is dissipatively transferred from the occupied states below the superconducting gap to the empty states above the superconducting gap. By computing the currents in the presence of weak inelastic relaxation, the authors establish the voltage threshold below which the equilibrium occupations of the Andreev states are restored, and the transconductances reach their quantized values. The results are an important step towards experimental verification of the topological properties of multiterminal Josephson junctions.