Half-filled Landau level, topological insulator surfaces, and three dimensional quantum spin liquids

Abstract

We synthesize and partly review recent developments relating the physics of the half-filled Landau level in two dimensions to correlated surface states of topological insulators in three dimensions. The latter are in turn related to the physics of certain three dimensional quantum spin liquid states. The resulting insights provide an interesting answer to the old question of how particle-hole symmetry is realized in composite fermion liquids. Specifically the metallic state at filling $\nu =\frac{1}{2}$ - described originally in pioneering work by Halperin , Lee, and Read as a liquid of composite fermions - was proposed recently by Son to be described by a particle-hole symmetric effective field theory distinct from that in the prior literature. We show how the relation to topological insulator surface states leads to a physical understanding of the correctness of this proposal. We develop a simple picture of the particle-hole symmetric composite fermion through a modification of older pictures as electrically neutral "dipolar" particles. We revisit the phenomenology of composite fermi liquids (with or without particle-hole symmetry), and show that their heat/electrical transport dramatically violates the conventional Wiedemann-Franz law but satisfies a modified one. We also discuss the implications of these insights for finding physical realizations of correlated topological insulator surfaces.

22 pages, 7 figures; (v2) Added some clarifications and corrected typos

References in corpus (18)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Field Theory of Time-Reversal Invariant Insulators
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
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• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Is the Composite Fermion a Dirac Particle?
• Dual Dirac liquid on the surface of the electron topological insulator
• Three dimensional resonating valence bond liquids and their excitations
• Unusual liquid state of hard-core bosons on the pyrochlore lattice
• Particle-Hole Symmetry and the Composite Fermi Liquid
• Composite Dirac liquids: parent states for symmetric surface topological order
• Mirror symmetry and the half-filled Landau level
• Luttinger theorem for the strongly correlated Fermi liquid of composite fermions
• A controlled expansion for certain non-Fermi liquid metals
• Interacting surface states of three-dimensional topological insulators
• Model Realization and Numerical Studies of a Three-Dimensional Bosonic Topological Insulator and Symmetry-Enriched Topological Phases

Cited by in corpus (83)

• A Duality Web in 2+1 Dimensions and Condensed Matter Physics
• Deconfined quantum critical points: symmetries and dualities
• Particle-Vortex Duality from 3d Bosonization
• 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
• Symmetric-Gapped Surface States of Fractional Topological Insulators
• Anomaly Manifestation of Lieb-Schultz-Mattis Theorem and Topological Phases
• Duality between the deconfined quantum-critical point and the bosonic topological transition
• Composite Fermi Liquid at Zero Magnetic Field in Twisted MoTe${}_2$
• Particle-hole symmetry without particle-hole symmetry in the quantum Hall effect at ν = 5/2
• Bosonization and Mirror Symmetry
• The nature of composite fermions and the role of particle hole symmetry: A microscopic account
• Emergence of supersymmetric quantum electrodynamics
• Composite fermi liquids in the lowest Landau level
• Superconducting quantum criticality of topological surface states at three loops
• Particle-Hole Symmetry in the Fermion-Chern-Simons and Dirac Descriptions of a Half-Filled Landau Level
• Bulk-boundary correspondence for intrinsically-gapless SPTs from group cohomology
• Particle-Hole Symmetries in Condensed Matter
• Symmetry and duality in bosonization of two-dimensional Dirac fermions
• Composite fermion duality for half-filled multicomponent Landau Levels
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Phase transitions out of quantum Hall states in moiré materials
• Striped quantum Hall state in a half-filled Landau level
• Thermoelectric transport signatures of Dirac composite fermions in the half-filled Landau level
• Particle-hole symmetry and composite fermions in fractional quantum Hall states
• Lattice Monte Carlo for Quantum Hall States on a Torus
• Berry phase and model wavefunction in the half-filled Landau Level
• Realizing topological surface states in a lower-dimensional flat band
• Emergent particle-hole symmetry in the half-filled Landau level
• Non-commutative field theory and composite Fermi Liquids in some quantum Hall systems
• Symmetry enriched U(1) quantum spin liquids
• Bulk characterization of topological crystalline insulators: stability under interactions and relations to symmetry enriched U(1) quantum spin liquids
• Landau-Level Mixing and Particle-Hole Symmetry Breaking for Spin Transitions in the Fractional Quantum Hall Effect
• 3d Abelian Dualities with Boundaries
• Fractional $S$-duality, Classification of Fractional Topological Insulators and Surface Topological Order
• The Dirac Composite Fermion of the Fractional Quantum Hall Effect
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Quantum Hall hierarchy from coupled wires
• Dirac Fermion Hierarchy of Composite Fermi Liquids
• Geometric Resonance of Composite Fermions near Bilayer Quantum Hall States
• Emergent particle-hole symmetry in spinful bosonic quantum Hall systems
• A series of (2+1)d Stable Self-Dual Interacting Conformal Field Theories
• Bosonic Analogue of Dirac Composite Fermi Liquid
• Weiss oscillations and particle-hole symmetry at the half-filled Landau level
• Trial wave functions for a Composite Fermi liquid on a torus
• Surprising robustness of particle-hole symmetry for composite fermion liquids
• From Dirac semimetals to topological phases in three dimensions: a coupled wire construction
• Berry Phase and Anomalous Transport of the Composite Fermions at the Half-Filled Landau Level
• Capacity of entanglement and distribution of density matrix eigenvalues in gapless systems
• Particle-hole symmetry for composite fermions: An emergent symmetry in the fractional quantum Hall effect
• Particle-vortex symmetric liquid
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Upper bounds on superconducting and excitonic phase-stiffness for interacting isolated narrow bands
• Entanglement entropy of composite Fermi liquid states on the lattice: In support of the Widom formula
• Berry phase of the composite-fermion Fermi Sea: Effect of Landau-level mixing
• Precise Experimental Test of the Luttinger Theorem and Particle-Hole Symmetry for a Strongly Correlated Fermionic System
• Geometric Resonance of Four-Flux Composite Fermions
• The Dirac composite fermion of the fractional quantum Hall effect
• Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems
• Parity anomaly cancellation in a three-dimensional QED with single massless Dirac fermion
• Lowest Landau level theory of the bosonic Jain states
• Non-Abelian Fermionization and Fractional Quantum Hall Transitions
• Partial filled Landau Level at even denominator, a vortex metal with Berry phase
• Pairing of particle-hole symmetric composite fermions in half-filled Landau level
• Paired parton quantum Hall states: a coupled wire construction
• Cyclotron Orbits of Composite Fermions in the Fractional Quantum Hall Regime
• Surfaces and Slabs of Fractional Topological Insulator Heterostructures
• Emergent Gauge Fields in Band Insulators
• Thermopower and Nernst measurements in a half-filled lowest Landau level
• Pairing instabilities of Dirac composite fermions
• Semiclassical theory of the tunneling anomaly in partially spin-polarized compressible quantum Hall states
• Unveiling Correlated Two-dimensional Topological Insulators through Fermionic Tensor Network States -- Classification, Edge Theories and Variational Wavefunctions
• Gapless state of interacting Majorana fermions in a strain-induced Landau level
• Quantum Hall bilayer in dipole representation
• Boson-fermion duality in four dimensions
• Thermoelectric properties and Wiedemann-Franz like relations in mixed-dimensional QEDs from particle-vortex dualities
• On S-duality for holographic p-wave superconductors
• Nonperturbative emergence of Dirac fermion in strongly correlated composite fermions of fractional quantum Hall effects
• "Self-Dual" Quantum Critical Point on the surface of $3d$ Topological Insulator
• Fermionic skyrmions and bosonization for a Gross-Neveu transition
• Giga fine-structure constant in photonic solitons
• Viewpoint: duality for fermionic vortices
• Emergence of Dirac Composite Fermions: Dipole Picture