Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus

Abstract

Recent quantum Hall experiments have observed `daughter states' next to several plateaus at half-integer filling factors in various platforms. These states were first proposed based on model wavefunctions for the Moore-Read state by Levin and Halperin. We show that these daughters and their parents belong to an extensive family tree that encompasses all pairing channels and permits a unified description in terms of weakly interacting composite fermions. Each daughter represents a bosonic integer quantum Hall state formed by composite-fermion pairs. The pairing of the parent dictates an additional number of filled composite-fermion Landau levels. We support our field-theoretic composite-fermion treatment by using the K-matrix formalism, analysis of trial wavefunctions, and a coupled-wire construction. Our analysis yields the topological orders, quantum numbers, and experimental signatures of all daughters of paired states at half-filling and `next-generation' even-denominators. Crucially, no two daughters share the same two parents. The unique parentage implies that Hall conductance measurements alone could pinpoint the topological order of even-denominator plateaus. Additionally, we propose a numerically suitable trial wavefunction for one daughter of the SU(2)${}_2$ topological order, which arises at filling factor $\nu =\frac{6}{11}$. Finally, our insights explain experimentally observed features of transitions in wide-quantum wells, such as suppression of the Jain states with the simultaneous development of half-filled and daughter states.

arXiv comment11 pages, 4 figures

References in corpus (93)

• 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
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Topological orders and Edge excitations in FQH states
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Riemannian symmetric superspaces and their origin in random matrix theory
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• Non-Abelian adiabatic statistics and Hall viscosity in quantum Hall states and p_x+ip_y paired superfluids
• Particle-hole symmetry and the Pfaffian state
• Viscosity of Quantum Hall Fluids
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Observation of half-integer thermal Hall conductance
• Transition from quantum Hall to compressible states in the second Landau level: new light on the $\nu$=5/2 enigma
• Incompressible paired Hall state, stripe order and the composite fermion liquid phase in half-filled Landau levels
• Are non-Fermi-liquids stable to Cooper pairing?
• The Fractional Quantum Hall effect in an array of quantum wires
• Robust fractional quantum Hall states and continuous quantum phase transitions in a half-filled bilayer graphene Landau level
• From Luttinger liquid to non-Abelian quantum Hall states
• Quantum Hall Physics - hierarchies and CFT techniques
• Observation of neutral modes in the fractional quantum Hall regime
• Integer quantum Hall effect for bosons: A physical realization
• Observed Quantization of Anyonic Heat Flow
• Nonconventional odd denominator fractional quantum Hall states in the second Landau level
• Classification and analysis of two dimensional abelian fractional topological insulators
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
• Even denominator fractional quantum Hall state in bilayer graphene
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• Observation of even denominator fractional quantum Hall effect in suspended bilayer graphene
• Even denominator fractional quantum Hall states at an isospin transition in monolayer graphene
• Finite Layer Thickness Stabilizes the Pfaffian State for the 5/2 Fractional Quantum Hall Effect: Wavefunction Overlap and Topological Degeneracy
• Fractional Quantum Hall Hierarchy and the Second Landau Level
• Density Matrix Renormalization Group Study of Incompressible Fractional Quantum Hall States
• The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
• Breaking of Particle-Hole Symmetry by Landau Level Mixing in the nu=5/2 Quantized Hall State
• Real-Space Entanglement Spectrum of Quantum Hall States
• Even denominator fractional quantum Hall states in higher Landau levels of graphene
• Landau level mixing and the emergence of Pfaffian excitations for the 5/2 fractional quantum Hall effect
• Tunneling of anyonic Majorana excitations in topological superconductors
• Real-space entanglement spectrum of quantum Hall systems
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Possibility of p-wave pairing of composite fermions at $\nu =1/2$
• Parton construction of a wave function in the anti-Pfaffian phase
• Quantum Phase Transition between Integer Quantum Hall States of Bosons
• Isolated Ballistic Non-Abelian Interface Channel
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Novel method distinguishing between competing topological orders
• Valley Isospin Controlled Fractional Quantum Hall States in Bilayer Graphene
• Lorentz shear modulus of a two-dimensional electron gas at high magnetic field
• Observation of a Fractional Quantum Hall State at $\nu =1/4$ in a Wide GaAs Quantum Well
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Electronic transport in an array of quasi-particles in the nu=5/2 non-abelian quantum Hall state
• Prediction of a non-Abelian fractional quantum Hall state with $f$-wave pairing of composite fermions in wide quantum wells
• Two-dimensional quantum liquids from interacting non-Abelian anyons
• Topological classification of shot noise on fractional quantum Hall edges
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• Observation of fractional quantum Hall effect at even-denominator 1/2 and 1/4 fillings in asymmetric wide quantum wells
• Majorana fermions in vortex lattices
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Collective states of non-abelian quasiparticles in a magnetic field
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Exact realization of Integer and Fractional Quantum Hall Phases in U(1)xU(1) models in (2+1)d
• A cascade of phase transitions in an orbitally mixed half-filled Landau level
• Fractional Quantum Hall Effect at $\nu =2+6/13$: The Parton Paradigm for the Second Landau Level
• Energy gap of the even-denominator fractional quantum Hall state in bilayer graphene
• Majorana fermions on a disordered triangular lattice
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• Entanglement Spectrum of Composite Fermion States in Real Space
• Quantum Hall hierarchy from coupled wires
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Even-Denominator Fractional Quantum Hall State at Filling Factor ν = 3/4
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Composite-fermion pairing at half and quarter filled lowest Landau level
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Composite fermion pairing induced by Landau level mixing
• $\nu =1/2$ Fractional Quantum Hall Effect in Tilted Magnetic Fields
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Real-space entanglement spectra of parton states in fractional quantum Hall systems
• Topological phase transition between composite-fermion and Pfaffian daughter states near ν = 1/2 FQHS
• Self-Consistent Electron Subbands of Gaas/Algaas Heterostructure in Magnetic Fields Parallel to the Interface
• Binding Transition in Quantum Hall Edge States
• Unification of parton and coupled-wire approaches to quantum magnetism in two dimensions
• Phase diagram of superconductivity in the integer quantum Hall regime
• Fractional quantum Hall effect of partons and the nature of the 8/17 state in the zeroth Landau level of bilayer graphene
• Identifying non-Abelian anyons with upstream noise
• Interacting Edge States of Fermionic Symmetry-Protected Topological Phases in Two Dimensions
• Conformal field theory approach to parton fractional quantum Hall trial wave functions
• Transport Signatures of Fractional Quantum Hall Binding Transitions
• Real-space entanglement spectra of projected fractional quantum Hall states using Monte Carlo methods

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• Quarter- and half-filled quantum Hall states and their topological orders revealed by daughter states in bilayer graphene
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• Universal charge conductance at Abelian--non-Abelian quantum Hall interfaces
• Non-Abelian phases from the condensation of Abelian anyons
• Ordering the topological order in the fractional quantum Hall effect
• Even-denominator fractional quantum Hall states in the zeroth Landau level of ABA trilayer graphene