Identifying the $\nu=\frac{5}{2}$ topological order through charge transport measurements

Understand

We propose an experiment to identify the topological order of the $\nu=\frac{5}{2}$ state through a measurement of the electric conductance of a mesoscopic device.

• Our setup is based on interfacing $\nu=2, \ \frac{5}{2}$ and $3$ in the same device.
• Its conductance can unambiguously establish or rule out the particle-hole symmetric Pfaffian topological order, which is supported by recent thermal measurements.
• Additionally, it distinguishes between the Moore-Read and Anti-Pfaffian topological orders, which are favored by numerical calculations.