Interfacial Conductance at the ν = 5/2 Quantum Hall State

The fractional quantum Hall state at filling factor 𝜈 = 5/2 is believed to exhibit non-Abelian braiding statistics. Identifying the exact topological order in physical two-dimensional systems remains a challenging and unresolved issue. Here, we report on measurements of interfacial charge conductance measurement in a topology equivalent π-shaped geometry in which two different filling factors are brought into close proximity to the examined ν = 5/2 state [1,2]. We have measured the conductance along these interfaces while varying the interaction region length from 1 μm to 8 μm and find that measured conductance is best described in incoherent limit down to the length scale L = 2.5 μm. For a device with an interaction region length of L = 1.0 μm, the measured conductance differs from the incoherent limit as well as from Moore-Read Pfaffian (MR-Pf) and it's particle-hole conjugate (anti-Pfaffian, A-Pf) state. Our initial results appear most consistent with the particle-hole invariant Pfaffian (PH-Pf).

[1] M. Yutushui, A. Stern, D. F. Mross, Phys. Rev. Lett. 128, 016401 (2022)

[2] M. Yutushui, A. Stern, D. F. Mross, Phys. Rev. Lett. 134, 206301 (2025)