Theory of Disorder-Induced Half-Integer Thermal Hall Conductance

Abstract

Electrons that are confined to a single Landau level in a two dimensional electron gas realize the effects of strong electron-electron repulsion in its purest form. The kinetic energy of individual electrons is completely quenched and all physical properties are dictated solely by many-body effects. A remarkable consequence is the emergence of new quasiparticles with fractional charge and exotic quantum statistics of which the most exciting ones are non-Abelian quasiparticles. A non-integer quantized thermal Hall conductance ${\kappa }_{xy}$ (in units of temperature times the universal constant ${\pi }^2{k}_B^2/3h$; $h$ is the Planck constant and $k_B$ the Boltzmann constant) necessitates the existence of such quasiparticles. It has been predicted, and verified numerically, that such states are realized in the clean half-filled first Landau level of electrons with Coulomb repulsion, with ${\kappa }_{xy}$ being either $3/2$ or $7/2$. Excitingly, a recent experiment has indeed observed a half-integer value, which was measured, however, to be ${\kappa }_{xy}=5/2$. We resolve this contradiction within a picture where smooth disorder results in the formation of mesoscopic puddles with locally ${\kappa }_{xy}=3/2$ or $7/2$. Interactions between these puddles generate a coherent macroscopic state, which is reflected in an extended plateau with quantized ${\kappa }_{xy}=5/2$. The topological properties of quasiparticles at large distances are determined by the macroscopic phase, and not by the microscopic puddle where they reside. In principle, the same mechanism might also allow non-Abelian quasiparticles to emerge from a system comprised of microscopic Abelian puddles.

8 pages, 8 figures

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Cited by in corpus (78)

• Observation of half-integer thermal Hall conductance
• Duality between $(2+1)d$ Quantum Critical Points
• Fractional charge and fractional statistics in the quantum Hall effects
• Isolated Ballistic Non-Abelian Interface Channel
• Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State
• Novel method distinguishing between competing topological orders
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• Real-space representation of winding number for one-dimensional chiral-symmetric topological insulator
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Comment on S. H. Simon, Interpretation of thermal conductance of the $\nu =5/2$ edge, arXiv:1801.09687
• Numerical exploration of trial wave functions for the particle-hole-symmetric Pfaffian
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Graviton Chirality and Topological Order in the Half-filled Landau Level
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Energetics of Pfaffian-AntiPfaffian Domains
• Phenomenological theory of heat transport in the fractional quantum Hall effect
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Temperature enhancement of thermal Hall conductance quantization
• Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
• Edge Probes of Topological Order
• Optimal thermoelectricity with quantum spin-Hall edge states
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Quantum Hall hierarchy from coupled wires
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Energy relaxation in edge modes in the quantum Hall effect
• Spin liquids from Majorana Zero Modes in a Cooper Box
• The chiral SYK model
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• Energetics of the PH-Pfaffian state and the 5/2-fractional quantum Hall effect
• Cooling low-dimensional electron systems into the microkelvin regime
• Disorder-driven transition and intermediate phase for $\nu =5/2$ fractional quantum Hall effect
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Boundary central charge from bulk odd viscosity - chiral superfluids
• Hong-Ou-Mandel heat noise in the quantum Hall regime
• An Effective Field Theory for Fractional Quantum Hall Systems near $\nu =5/2$
• Aspects of Three-body Interactions in Generic Fractional Quantum Hall Systems and Impact of Galilean Invariance Breaking
• Mesoscopic valley filter in graphene Corbino disk containing a p-n junction
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
• Thermal drag effect in quantum Hall circuits
• Geometric responses of the Pfaffian state
• Non-Abelian quasiholes in lattice Moore-Read states and parent Hamiltonians
• Simple analog of the black-hole information paradox in quantum Hall interfaces
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength
• PH-Pfaffian order in a translationally and rotationally invariant system
• Measuring Topological Order
• Model wavefunctions for interfaces between lattice Laughlin states
• Model interactions for Pfaffian paired states based on Chern-Simons field theory description
• Paired parton quantum Hall states: a coupled wire construction
• Domain Formation Driven by the Entropy of Topological Edge Modes
• Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field
• Pfaffian paired states for half-integer fractional quantum Hall effect
• Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Dynamics of Quantum Hall Interfaces
• Phase diagram of compressible and paired states in the quarter-filled Landau level
• Disorder broadening of even denominator fractional quantum Hall states in the presence of a short-range alloy potential
• Gauging or extending bulk and boundary conformal field theories: Application to bulk and domain wall problem in topological matter and their descriptions by (mock) modular covariant
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• Domain Textures in the Fractional Quantum Hall Effect
• Renormalization-group-inspired neural networks for computing topological invariants
• Approximate half-integer quantization in anomalous planar transport in $d$-wave altermagnets
• Phase transitions and topological properties of the 5/2 quantum Hall states with strong Landau-level mixing
• Non-Abelian phases from the condensation of Abelian anyons
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Geometric and computational aspects of chiral topological quantum matter
• Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State
• Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Transmission line approach to transport of heat in chiral systems with dissipation
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids
• The Second Landau Level Projection of Antiholomorphic Pfaffian Wavefunctions