Phase transitions on the edge of the \nu=5/2 Pfaffian and anti-Pfaffian quantum Hall state

TL;DR

This paper investigates how interactions between edge modes in the =5/2 fractional quantum Hall state can induce phase transitions that gap Majorana modes, potentially explaining observed states without altering bulk topological order.

Contribution

It introduces the concept of Majorana-gapped phases on the edge of the =5/2 state, showing edge phase transitions without bulk topological change, a novel insight in FQH physics.

Findings

Interactions induce edge phase transitions in =5/2 states.

Quasiparticle tunneling exponents change in new phases.

Majorana-gapped phases are candidate states for observed phenomena.

Abstract

Starting from the edge reconstructed Pfaffian state and the anti-Pfaffian state for the filling fraction $\nu={5/2}$ fractional quantum Hall (FQH) state with the filled Landau levels included, we find that interactions between counterpropagating edge modes can induce phase transitions on the edge. In the new `Majorana-gapped' phases, a pair of counter propagating neutral Majorana modes becomes gapped. The quasiparticle tunneling exponent changes from $g=1/4$ to $g=1/2$ for the edge reconstructed Pfaffian state, and changes from $g=1/2$ to $g=0.55-0.75$ for the anti-Pfaffian state, in the new Majorana-gapped phases. The new phases are candidate states for the observed $\nu={5/2}$ state. Furthermore, Majorana-gapped phases provide examples that non-trivial quantum phase transitions can happen on the edge of a FQH state without any change in bulk topological order.