Topological pairing of composite fermions via criticality

TL;DR

This paper investigates the topological origin of pairing in composite fermions at the 5/2 fractional quantum Hall state, revealing a critical point where Majorana fermions deconfine, leading to non-Abelian paired states.

Contribution

It introduces an effective dipole framework to explain pairing driven by topological band properties and describes the critical behavior and deconfinement of Majorana fermions in this context.

Findings

Pairing is linked to the topology of the Landau level band.

A critical point with deconfined Majorana fermions is analytically described.

Short-range interactions can stabilize a Fermi-liquid-like state, but slow-decay pseudopotentials favor pairing.

Abstract

The fractional quantum Hall effect (FQHE) at the filling factor with an even denominator, 5/2, occurs despite the expectation, due to the electron statistics, that the denominator must be an odd number. It is believed that the Cooper pairing of underlying quasiparticles, composite fermions (CFs), leads to the explanation of this effect. Such a state should have a Pfaffian form of the BCS wave function (due to the absence of spin) and non-Abelian statistics of possible vortex-like excitations (due to the $p$-wave nature of the pairing). Here we expose the origin of pairing by using the effective dipole representation of the problem and show that pairing is encoded in a Hamiltonian that describes the interaction of the charge density with dipoles i.e. the current of CFs. The necessary condition for the paired state to exist is the effective dipole physics at the Fermi level as a consequence of the non-trivial topology of the ideal band in which electrons live - a Landau level (LL); the paired state is a resolution of the unstable, critical behaviour characterized by the distancing of correlation hole with respect to electron (and thus dipole) at the Fermi level due to the topology. We describe analytically this deconfined critical point, at which deconfinement of Majorana neutral fermions takes place. In the presence of large, short-range repulsive interaction inside a LL, the critical behavior may be stabilized into a regularized Fermi-liquid-like (FLL) state, like the one that characterizes the physics in the lowest LL (LLL), but in general, for an interaction with slowly decaying pseudopotentials, the system is prone to pairing.