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

We propose an experiment to identify the topological order of the $ν=\frac{5}{2}$ state through a measurement of the electric conductance of a mesoscopic device. Our setup is based on interfacing $ν=2, \ \frac{5}{2}$ 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.

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