DC Conductance of X-shaped Majorana Interferometer reveals Non-Abelian Anyon Statistics

We propose a four-terminal, X-shaped chiral Majorana interferometer with a central floating superconducting island, enabling the direct detection of the non-Abelian statistics of Ising anyons via the linear-response DC conductance tensor in charge transport experiments. Here, Ising anyons are realizable as edge vortices nucleated at Josephson line junctions defining the superconducting island, where both edge-vortex and Majorana-fermion tunneling processes can occur. We show that in such a multi-terminal Majorana interferometer, both the vacuum and the fermionic fusion channel for Ising anyons are possible. This is in contrast to two-arm interferometers, where only the vacuum fusion channel is accessible and the DC conductance contribution from edge vortices always vanishes. Using a low-energy effective theory derived via chiral bosonization, we find that in the X-shaped interferometer, the DC conductance tensor is completely isotropic, yielding a non-zero conductance when simultaneous edge-vortex and Majorana tunneling activates the fermionic fusion channel. Apart from conductance oscillations in a gate-tunable charge parameter, which display an offset related to the anyon topological spin, measuring a finite conductance can already provide direct evidence for non-Abelian statistics in this geometry.