$\varphi$ Josephson junction induced by altermagnetism

TL;DR

This paper explores the Josephson effect in superconductor/altermagnet/superconductor junctions, revealing novel phenomena like 0-$\

Contribution

It introduces the concept of $\

Findings

Observation of 0-$\pi$ transition

Support for $\

Demonstration of tunable $\

Abstract

We study the Josephson effect in a superconductor/altermagnet/superconductor (S/AM/S) junction. We find anomalous phenomena including $0$-$\pi$ transition as well as multi-nodal current-phase relations. Similar to $d$-wave superconductor, $d$-wave altermagnet can support $\varphi$ junction where free energy minima locate neither $\varphi=0$ nor $\pm \pi$ with double degeneracy. These properties can be tunable by parameters, e.g., the exchange energy, the orientation of crystal axis, the length, and the chemical doping of altermagnet. These rich features lead to accessible functionality of S/AM/S junction.