Stabilization of the Particle-Hole Pfaffian Order by Landau-Level Mixing and Impurities That Break Particle-Hole Symmetry

Numerical results suggest that the quantum Hall effect at $\nu =5/2$ is described by the Pfaffian or anti-Pfaffian state in the absence of disorder and Landau-level mixing. Those states are incompatible with the observed transport properties of GaAs heterostructures, where disorder and Landau-level mixing are strong. We show that the recent proposal of a particle-hole (PH)-Pfaffian topological order by Son is consistent with all experiments. The absence of particle-hole symmetry at $\nu =5/2$ is not an obstacle to the existence of the PH-Pfaffian order since the order is robust to symmetry breaking.

Figure 1

Aharonov-Bohm interferometer. Quasiparticles move along the edges and tunnel between the edges at the quantum point contacts QPC1 and QPC2. Several quasiparticles are localized inside the device.

Figure 2

Mach-Zehnder interferometer.

Figure 3

The nodes show the superselection sectors of the drain $D2$. The arrows show all of the possible transitions between the sectors. The transition probabilities are written next to the arrows.