Nonreciprocal Equilibrium Josephson Effect of Arbitrary Periodicity from Poor Man's Majorana Zero Modes

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. This PMM regime is accompanied by 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 Josephson current can possess any periodicity in equilibrium, including $4\pi$. Our work opens the door to observing and harnessing Majorana behavior in currently experimentally accessible topologically trivial systems.