Topological pairing of composite fermions via criticality

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.

18 pages, 7 figures, 5 appendices

References in corpus (13)

• Non-Abelian Anyons and Topological Quantum Computation
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Composite fermion theory of rapidly rotating two-dimensional bosons
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Fermions out of Dipolar Bosons in the lowest Landau level
• Observable signatures of Hall viscosity in lowest Landau level superfluids
• Dipole representation of half-filled Landau level
• Incompressible Liquid, Stripes and Bubbles in rapidly rotating Bose atoms at $\nu =1$
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• Large composite fermion effective mass at filling factor 5/2

Cited by in corpus (2)

• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Dipole representation of composite fermions in graphene quantum Hall systems