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

The central challenge in topological quantum computing is the experimental verification of non-Abelian braiding statistics. While Ising anyons—vortices harboring Majorana zero modes—are predicted to exist in chiral Majorana edge states, detecting their non-Abelian nature remains difficult. Previous two-arm interferometer designs are limited because they only access the vacuum fusion channel, causing the DC conductance contribution from edge vortices to vanish. This paper investigates whether a more complex, four-terminal X-shaped interferometer can overcome these limitations to provide a measurable signature of non-Abelian statistics.

The authors propose an X-shaped device formed on the surface of a topological insulator, proximitized by a central floating superconducting island. This island is defined by four Josephson line junctions where edge vortices and Majorana fermions can tunnel. By utilizing a low-energy effective theory based on chiral bosonization, the researchers model the transport of these "flying" Ising anyons. They analyze the system in both weak- and strong-coupling regimes to derive the linear-response DC conductance tensor, specifically looking for signals that distinguish the fermionic fusion channel from the vacuum channel.

The analysis reveals that the X-shaped geometry successfully activates the fermionic fusion channel, which is inaccessible in simpler two-arm designs. The resulting DC conductance tensor is found to be completely isotropic and non-zero, providing a direct experimental observable for non-Abelian statistics. Furthermore, the conductance exhibits oscillations dependent on a gate-tunable charge parameter, with an offset directly related to the topological spin of the Ising anyons. This suggests that measuring a finite DC conductance in this specific configuration constitutes clear evidence of non-Abelian braiding.