This paper proposes a new, highly controllable device for creating and moving Majorana corner modes. Majorana zero modes are exotic electronic states that many researchers hope to use for fault‑tolerant quantum computing. The authors show, in theory and numerical models, that a Josephson junction whose weak link is an altermagnet can host these corner modes and that two independent controls — the superconducting phase difference and the direction of the altermagnet’s Néel vector (the axis of its antiferromagnetic order) — can be used to steer the modes from one corner of a fixed sample to another.

The device is a conventional‑superconductor — altermagnet — conventional‑superconductor sandwich, with the phase difference ϕ between the superconductors set by magnetic flux. At a π phase bias the junction realizes a two‑dimensional topological superconducting state along its edges. The authors add an altermagnetic spin splitting in the weak link and show that, depending on the Néel‑vector orientation and the phase ϕ, this spin splitting opens or closes a gap along different edges. Where the sign of that edge gap changes between neighboring edges, bound states localize at the corners — the Majorana corner modes (MCMs). The paper presents a phase diagram in the (ϕ, φ) plane (φ is the Néel azimuthal angle) showing distinct regions with MCMs at selected corner pairs.

A key result is that sweeping the two control knobs reshapes the effective “boundary mass” and can deterministically relocate an MCM from one corner to another without changing the sample geometry. That motion produces a concrete experimental fingerprint: local tunneling into a corner should show a quantized zero‑bias conductance peak of 2e^2/h at the corner holding an MCM and a simultaneous disappearance of that peak at the corner the mode left. Because trivial Andreev bound states caused by local defects tend to stay pinned to their defect sites, they cannot reproduce this macroscopic, phase‑locked switching of conductance. The authors therefore argue this control‑correlated conductance switching is an unambiguous diagnostic for true Majorana corner modes.