Nonreciprocal Equilibrium 4$\pi$-Periodic Josephson Effect from Poor Man's Majorana Zero Modes

TL;DR

This paper demonstrates a nonreciprocal Josephson diode effect arising from poor man's Majorana states in a system of magnetic adatoms on a superconductor, revealing new topological phenomena in trivial systems.

Contribution

It introduces a novel mechanism for the Josephson diode effect via PMM excitations and shows $4 ext{π}$-periodic Josephson behavior in a topologically trivial setup.

Findings

Significant nonreciprocity when YSR states approach zero energy.

Control of diode efficiency through adatom configuration.

Observation of $4 ext{π}$-periodic Josephson effect in trivial systems.

Abstract

We show that the Josephson diode effect becomes possible when two coupled antiferromagnetic dimers of point-like magnetic adatoms are deposited on top of a Rashba superconductor. The degree of nonreciprocity is substantial when the arising Yu-Shiba-Rusinov (YSR) bound states approach zero energy. In this limit, these states behave as weakly coupled poor man's Majorana (PMM) excitations. The emergence of PMMs leads to highly dispersive and phase-bias asymmetric Andreev bound state dispersions. In turn, these result in a nonreciprocal Josephson current, whose diode efficiency can be controlled by varying the geometric details of the adatom's spatial configuration. In addition, thanks to spin-triplet pairing terms mixing different YSR states, the resulting Josephson effect is $4\pi$-periodic even under equilibrium conditions. Our work opens the door to observing and harnessing Majorana behavior in currently experimentally accessible topologically trivial systems.