Beyond the standard model of topological Josephson junctions: From crystalline anisotropy to finite-size and diode effects

TL;DR

This paper explores complex behaviors in topological Josephson junctions, revealing nonuniversal effects due to anisotropy, finite size, and spin-orbit coupling, with implications for quantum computing and superconducting spintronics.

Contribution

It uncovers nonuniversal phenomena in topological Josephson junctions beyond standard models, emphasizing the roles of anisotropy, finite size, and Dresselhaus spin-orbit coupling.

Findings

Zeeman field for phase jump differs from that for critical current minimum.

Finite width and Dresselhaus coupling cause nonuniversal topological behaviors.

Josephson junctions exhibit nonreciprocal transport and superconducting diode effects.

Abstract

A planar Josephson junction is a versatile platform to realize topological superconductivity over a large parameter space and host Majorana bound states. With a change in Zeeman field, this system undergoes a transition from trivial to topological superconductivity accompanied by a jump in the superconducting phase difference between the two superconductors. A standard model of these Josephson junctions, which can be fabricated to have a nearly perfect interfacial transparency, predicts a simple universal behavior. In that model, at the same value of Zeeman field for the topological transition, there is a $\pi$ phase jump and a minimum in the critical superconducting current, while applying a controllable phase difference yields a diamond-shaped topological region as a function of that phase difference and a Zeeman field. In contrast, even for a perfect interfacial transparency, we find a much richer and nonuniversal behavior as the width of the superconductor is varied or the Dresselhaus spin-orbit coupling is considered. The Zeeman field for the phase jump, not necessarily $\pi$, is different from the value for the minimum critical current, while there is a strong deviation from the diamond-like topological region. These Josephson junctions show a striking example of a nonreciprocal transport and superconducting diode effect, revealing the importance of our findings not only for topological superconductivity and fault-tolerant quantum computing, but also for superconducting spintronics.