Topological Order from Disorder and the Quantized Hall Thermal Metal: Possible Applications to the $\nu =5/2$ State

Abstract

Although numerical studies modeling the quantum hall effect at filling fraction $5/2$ predict either the Pfaffian (Pf) or its particle hole conjugate, the anti-Pfaffian (aPf) state, recent experiments appear to favor a quantized thermal hall conductivity with quantum number $K=5/2$ , rather than the value $K=7/2$ or $K=3/2$ expected for the Pf or aPF state, respectively. While a particle hole symmetric topological order (the PH-Pfaffian) would be consistent with the experiments, this state is believed to be energetically unfavorable in a homogenous system. Here we study the effects of disorder that are assumed to locally nucleate domains of Pf and aPf. When the disorder is relatively weak and the size of domains is relatively large, we find that when the electrical Hall conductance is on the quantized plateau with ${\sigma }_{xy}=(5/2)(e^2/h)$, the value of $K$ can be only 7/2 or 3/2, with a possible first-order-like transition between them as the magnetic field is varied. However, for sufficiently strong disorder an intermediate state might appear, which we analyze within a network model of the domain walls. Predominantly, we find a thermal metal phase, where $K$ varies continuously and the longitudinal thermal conductivity is non-zero, while the electrical Hall conductivity remains quantized at $(5/2)e^2/h$. However, in a restricted parameter range we find a thermal insulator with $K=5/2$, a disorder stabilized phase which is adiabatically connected to the PH-Pfaffian. We discuss a possible scenario to rationalize these special values of parameters.

Slightly updated version with additional references, 12 pages + references, 9 figures

References in corpus (10)

• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Infinite density matrix renormalization group for multicomponent quantum Hall systems
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Spin polarization of the $\nu =5/2$ quantum Hall state
• Composite Dirac liquids: parent states for symmetric surface topological order
• Quantum phase transition of chiral Majorana fermion in the presence of disorder
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• Interface and Phase Transition between Moore-Read and Halperin 331 Fractional Quantum Hall States: Realization of Chiral Majorana Fermion

Cited by in corpus (70)

• Observation of half-integer thermal Hall conductance
• Fractional charge and fractional statistics in the quantum Hall effects
• Theory of Disorder-Induced Half-Integer Thermal Hall Conductance
• Parton construction of a wave function in the anti-Pfaffian phase
• Isolated Ballistic Non-Abelian Interface Channel
• Novel method distinguishing between competing topological orders
• Theory of Disordered $\nu =5/2$ Quantum Thermal Hall State: Emergent Symmetry and Phase Diagram
• 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
• Recovery of massless Dirac fermions at charge neutrality in strongly interacting twisted bilayer graphene with disorder
• Paired states at 5/2: PH Pfaffian and particle-hole symmetry breaking
• Temperature enhancement of thermal Hall conductance quantization
• Probing the spin structure of the fractional quantum Hall magnetoroton with polarized Raman scattering
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Topological Interface between Pfaffian and anti-Pfaffian Order in $\nu =5/2$ Quantum Hall Effect
• Large-scale simulations of particle-hole-symmetric Pfaffian trial wavefunctions
• Edge Probes of Topological Order
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Quantum Hall hierarchy from coupled wires
• Spin liquids from Majorana Zero Modes in a Cooper Box
• Energy relaxation in edge modes in the quantum Hall effect
• Intrinsic sign problem in fermionic and bosonic chiral topological matter
• The chiral SYK model
• 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
• Hong-Ou-Mandel heat noise in the quantum Hall regime
• Boundary central charge from bulk odd viscosity - chiral superfluids
• Subdiffusive dynamics and critical quantum correlations in a disorder-free localized Kitaev honeycomb model out of equilibrium
• 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
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
• 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
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• 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
• 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
• Model interactions for Pfaffian paired states based on Chern-Simons field theory description
• Model wavefunctions for an interface between lattice Laughlin and Moore-Read states
• Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction
• Pfaffian paired states for half-integer fractional quantum Hall effect
• 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
• Dynamics of Quantum Hall Interfaces
• Fermionic fractional quantum Hall states: A modern approach to systems with bulk-edge correspondence
• 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
• Energy minimization of paired composite fermion wave functions in the spherical geometry
• Domain Textures in the Fractional Quantum Hall Effect
• Geometric and computational aspects of chiral topological quantum matter
• Phase transitions and topological properties of the 5/2 quantum Hall states with strong Landau-level mixing
• Mean field approximations for short range four body interactions at $\nu =3/5$
• Real-Time Ramsey Interferometry in Fractional Quantum Hall States
• Composite fermion mass enhancement and particle-hole symmetry of fractional quantum Hall states in the lowest Landau level under realistic conditions
• Enigmatic 2+6/13 Filling Factor: A Prototype Intermittent Topological State
• Homomorphism, substructure, and ideal: Elementary but rigorous aspects of renormalization group or hierarchical structure of topological orders
• Edge Induced Topological Phase Transition of the Quantum Hall state at Half Filling
• Disorder-driven phase transitions in bosonic fractional quantum Hall liquids
• The Second Landau Level Projection of Antiholomorphic Pfaffian Wavefunctions