Particle-hole symmetry without particle-hole symmetry in the quantum Hall effect at {\nu} = 5/2

TL;DR

This paper demonstrates that the PH-Pfaffian topological order can exist at filling factor 5/2 in the quantum Hall effect, even without particle-hole symmetry, aligning with experimental observations in disordered GaAs systems.

Contribution

It shows that the PH-Pfaffian state is consistent with experiments despite particle-hole symmetry breaking, challenging previous assumptions about the necessity of symmetry for this order.

Findings

PH-Pfaffian order aligns with experimental data

Particle-hole symmetry is not essential for PH-Pfaffian stability

Disorder and Landau level mixing do not preclude PH-Pfaffian existence

Abstract

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 PH-Pfaffian topological order by Son is consistent with all experiments. The absence of the 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.