Composite fermion duality for half-filled multicomponent Landau Levels

Abstract

We study the interplay of particle-hole symmetry and fermion-vortex duality in multicomponent half-filled Landau levels, such as quantum Hall gallium arsenide bilayers and graphene. For the $\nu =1/2+1/2$ bilayer, we show that particle-hole-symmetric interlayer Cooper pairing of composite fermions leads to precisely the same phase as the electron exciton condensate realized in experiments. This equivalence is easily understood by applying the recent Dirac fermion formulation of $\nu =1/2$ to two components. It can also be described by Halperin-Lee-Read composite fermions undergoing interlayer $p_x+i{p}_y$ pairing. An RG analysis showing strong instability to interlayer pairing at large separation $d\to \infty$ demonstrates that two initially-decoupled composite Fermi liquids can be smoothly tuned into the conventional bilayer exciton condensate without encountering a phase transition. We also discuss multicomponent systems relevant to graphene, derive related phases including a $Z_2$ gauge theory with spin-half visons, and argue for symmetry-enforced gaplessness under full SU$(N_f)$ flavor symmetry when the number of components $N_f$ is even.

arXiv comment24 pages, 4 figures

References in corpus (68)

• Anyons in an exactly solved model and beyond
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Landau level degeneracy and quantum Hall effect in a graphite bilayer
• Unconventional quantum Hall effect and Berry's phase of 2pi in bilayer graphene
• Topological phases of fermions in one dimension
• Bose-Einstein Condensation of Excitons in Bilayer Electron Systems
• Spontaneous Inter-layer Coherence in Double-Layer Quantum-Hall Systems I: Charged Vortices and Kosterlitz-Thouless Phase Transitions
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Symmetry Protected Topological phases of Quantum Matter
• The effects of interactions on the topological classification of free fermion systems
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Coulomb-driven broken-symmetry states in doubly gated suspended bilayer graphene
• Spin and valley quantum Hall ferromagnetism in graphene
• Is the Composite Fermion a Dirac Particle?
• Determination of the gate-tunable bandgap and tight-binding parameters in bilayer graphene using infrared spectroscopy
• Electronic properties of bilayer and multilayer graphene
• Determination of the electronic structure of bilayer graphene from infrared spectroscopy results
• Tunable symmetry breaking and helical edge transport in a graphene quantum spin Hall state
• Are non-Fermi-liquids stable to Cooper pairing?
• Interacting fermionic topological insulators/superconductors in three dimensions
• Topological Disorder Operators in Three-Dimensional Conformal Field Theory
• Boson topological insulators: A window into highly entangled quantum phases
• Classification of interacting electronic topological insulators in three dimensions
• Particle-Vortex Duality from 3d Bosonization
• Particle-vortex duality of 2d Dirac fermion from electric-magnetic duality of 3d topological insulators
• Collective Modes and Skyrmion Excitations in Graphene SU(4) Quantum Hall Ferromagnets
• Phase diagram for the $\nu =0$ quantum Hall state in monolayer graphene
• Dual Dirac liquid on the surface of the electron topological insulator
• Accurate tight-binding and continuum models for the $\pi$ bands of bilayer graphene
• Evidence for a Spin Phase Transition at ν=0 in Bilayer Graphene
• Bosonic topological insulator in three dimensions and the statistical Witten effect
• Explicit derivation of duality between a free Dirac cone and quantum electrodynamics in (2+1) dimensions
• The half-filled Landau level: the case for Dirac composite fermions
• Electron-Hole Asymmetric Integer and Fractional Quantum Hall Effect in Bilayer Graphene
• Gauge Fields and Pairing in Double-Layer Composite Fermion Metals
• Canted antiferromagnetic phase of the $\nu =0$ quantum Hall state in bilayer graphene
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Strong Correlation to Weak Correlation Phase Transition in Bilayer Quantum Hall Systems
• Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids
• Bosonization and Mirror Symmetry
• Self-dual Quantum Electrodynamics as Boundary State of the three dimensional Bosonic Topological Insulator
• Phase Diagram for Quantum Hall Bilayers at $\nu =1$
• Composite fermi liquids in the lowest Landau level
• Time-reversal symmetric U(1) quantum spin liquids
• The Effects of Landau level mixing on the fractional quantum Hall effect in monolayer Graphene
• Bi-layer Paired Quantum Hall States and Coulomb Drag
• Fractional and integer quantum Hall effects in the zeroth Landau level in graphene
• Mirror symmetry and the half-filled Landau level
• Paired composite fermion phase of quantum Hall bilayers at ν= 1/2 + 1/2
• Trial Wavefunctions for ν= 1/2 + 1/2 Quantum Hall Bilayers
• SO(5) symmetry in the quantum Hall effect in graphene
• Broken SU(4) Symmetry and The Fractional Quantum Hall Effect in Graphene
• Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• Continuous transitions between composite Fermi liquid and Landau Fermi liquid: a route to fractionalized Mott insulators
• The $\nu =\frac{1}{2}$ Landau level: Half-full or half-empty?
• Emergent particle-hole symmetry in the half-filled Landau level
• Ground State of v=1 Bilayer Quantum Hall Systems
• Interlayer coherent composite Fermi liquid phase in quantum Hall bilayers
• Structure and the Lamb-shift-like quantum splitting of the pseudo-zero-mode Landau levels in bilayer graphene
• Renormalization and cyclotron resonance in bilayer graphene with weak electron-hole asymmetry
• Spontaneous Pseudospin Spiral Order in Bilayer Quantum Hall Systems
• Meron deconfinement in the quantum Hall bilayer at intermediate distances
• Nonperturbative approach to the quantum Hall bilayer
• Pairing instabilities of Dirac composite fermions
• Trial wavefunctions for the Goldstone mode in ν=1/2+1/2 quantum Hall bilayers

Cited by in corpus (41)

• Deconfined quantum critical points: symmetries and dualities
• Non-Invertible Duality Defects in 3+1 Dimensions
• Crossover between Strongly-coupled and Weakly-coupled Exciton Superfluids
• Obstructions to Gapped Phases from Non-Invertible Symmetries
• Anomaly Obstructions to Symmetry Preserving Gapped Phases
• Anomaly Constraints on Gapped Phases with Discrete Chiral Symmetry
• When Superconductivity Crosses Over: From BCS to BEC
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Realizing topological surface states in a lower-dimensional flat band
• On gapped boundaries for SPT phases beyond group cohomology
• Excitonic Laughlin States in Ideal Topological Insulator Flat Bands and Possible Presence in Moiré Superlattice Materials
• Precursors to Exciton Condensation in Quantum Hall Bilayers
• Numerical Study of Quantum Hall Bilayers at Total Filling ${\nu }_T=1$: A New Phase at Intermediate Layer Distances
• Deconfined metallic quantum criticality: A $U(2)$ gauge-theoretic approach
• Quantized axial charge of staggered fermions and the chiral anomaly
• Doping a fractional quantum anomalous Hall insulator
• $s$-wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with $\nu =1$
• Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers
• Upper bounds on superconducting and excitonic phase-stiffness for interacting isolated narrow bands
• XY* transition and extraordinary boundary criticality from fractional exciton condensation in quantum Hall bilayer
• Deconfined Metal-Insulator Transitions in Quantum Hall Bilayers
• Paired states in half-filled Landau levels
• Composite helical edges from Abelian fractional topological insulators
• Non-Abelian Fermionization and Fractional Quantum Hall Transitions
• Partial filled Landau Level at even denominator, a vortex metal with Berry phase
• Lattice Construction of Duality with Non-Abelian Gauge Fields in 2+1D
• Fermionic dualities with axial gauge fields
• Pairing of Composite-Electrons and Composite-Holes in ${\nu }_T=1$ Quantum Hall Bilayers
• Fractionalization as an alternate to charge ordering in electronic insulators
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
• Quantum Hall bilayer in dipole representation
• Single-parameter variational wavefunctions for quantum Hall bilayers
• Successive electron-vortex binding in quantum Hall bilayers at $\nu =\frac{1}{4}+\frac{3}{4}$
• Symmetry-Enforced Fermi Surfaces
• Ordering the topological order in the fractional quantum Hall effect
• On dualities of paired quantum Hall bilayer states at ${\nu }_T=\frac{1}{2}+\frac{1}{2}$
• Unnecessary quantum criticality in $SU(3)$ kagome magnets
• Analytic framework for self-dual criticality in ${\mathbb{Z}}_k$ gauge theory with matter
• Topology-driven deconfined quantum criticality in magnetic bilayers
• When Wannier centers jump: Critical points between atomic insulating phases
• Role of the compensating current in the weak Josphson coupling regime: An extended study on excitonic Josephson junctions