Thermal equilibration on the edges of topological liquids

Abstract

Thermal conductance has emerged as a powerful probe of topological order in the quantum Hall effect and beyond. The interpretation of experiments crucially depends on the ratio of the sample size and the equilibration length, on which energy exchange among contra-propagating chiral modes becomes significant. We show that at low temperatures the equilibration length diverges as $1/T^2$ for almost all Abelian and non-Abelian topological orders. A faster $1/T^4$ divergence is present on the edges of the non-Abelian PH-Pfaffian and negative-flux Read-Rezayi liquids. We address experimental consequences of the $1/T^2$ and $1/T^4$ laws in a sample, shorter than the equilibration length.

arXiv comment6 pages, 1 figure

References in corpus (28)

• Anyons in an exactly solved model and beyond
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Beyond paired quantum Hall states: parafermions and incompressible states in the first excited Landau level
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Particle-hole symmetry and the Pfaffian state
• Particle-Hole Symmetry and the $\nu =5/2$ Quantum Hall State
• Observation of half-integer thermal Hall conductance
• Is the Composite Fermion a Dirac Particle?
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Quantum limit of heat flow across a single electronic channel
• Electron correlation in the second Landau level; a competition between many, nearly degenerate quantum phases
• Impurity scattering and transport of fractional Quantum Hall edge state
• Observed Quantization of Anyonic Heat Flow
• Thermal Transport in Chiral Conformal Theories and Hierarchical Quantum Hall States
• A Time-Reversal Invariant Topological Phase at the Surface of a 3D Topological Insulator
• Experimental studies of the fractional quantum Hall effect in the first excited Landau level
• Quantum groups and nonabelian braiding in quantum Hall systems
• Particle-hole symmetry without particle-hole symmetry in the quantum Hall effect at ν = 5/2
• 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
• Non-Abelian states with negative flux: a new series of quantum Hall states
• Influence of device geometry on tunneling in ν=5/2 quantum Hall liquid
• Quantum Hall States at $\nu =\frac{2}{k+2}$
• Counter-propagating charge transport in the quantum Hall effect regime
• Phenomenological theory of heat transport in the fractional quantum Hall effect
• Experimental constraints and a possible quantum Hall state at $\nu =5/2$
• The sixteenfold way and the quantum Hall effect at half-integer filling factors
• Edge Probes of Topological Order

Cited by in corpus (13)

• Fractional charge and fractional statistics in the quantum Hall effects
• Isolated Ballistic Non-Abelian Interface Channel
• Novel method distinguishing between competing topological orders
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale
• Determination of topological edge quantum numbers of fractional quantum Hall phases
• Quantum Field Theory Anomalies in Condensed Matter Physics
• Heat equilibration of integer and fractional quantum Hall edge modes in graphene
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Possible restoration of particle-hole symmetry in the 5/2 Quantized Hall State at small magnetic field
• Approximate two-body generating Hamiltonian for the PH-Pfaffian wavefunction