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.

arXiv comment18 pages, 7 figures, 5 appendices

References in corpus (32)

• Non-Abelian Anyons and Topological Quantum Computation
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Rapidly Rotating Atomic Gases
• Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Quantum Hall fractions in rotating Bose-Einstein condensates
• Lowest-Landau-level theory of the quantum Hall effect: the Fermi-liquid-like state
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Theory of the half-filled Landau level
• A dipole interpretation of the $\nu =1/2$ state
• Parton construction of a wave function in the anti-Pfaffian phase
• Cooper Instability of Composite Fermions
• A continuous transition between fractional quantum Hall and superfluid states
• Particle Entanglement Spectra for Quantum Hall states on Lattices
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Non-commutative field theory and composite Fermi Liquids in some quantum Hall systems
• Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
• Composite fermion theory of rapidly rotating two-dimensional bosons
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Pomeranchuk Instability of Composite Fermi Liquids
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Paired states in half-filled Landau levels
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• Fermions out of Dipolar Bosons in the lowest Landau level
• Dipole representation of half-filled Landau level
• Incompressible Liquid, Stripes and Bubbles in rapidly rotating Bose atoms at $\nu =1$
• Observable signatures of Hall viscosity in lowest Landau level superfluids
• 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