Topological classification of shot noise on fractional quantum Hall edges

Abstract

Electrical and thermal transport on a fractional quantum Hall edge are determined by topological quantities inherited from the corresponding bulk state. While electrical transport is the standard method for studying edges, thermal transport appears more challenging. Here, we show that the shot noise generated on the edge provides a fully electrical method to probe the edge structure. In the incoherent regime, the noise falls into three topologically distinct universality classes: charge transport is always ballistic while thermal transport is either ballistic, diffusive, or "antiballistic". Correspondingly, the noise either vanishes, decays algebraically or is constant up to exponentially small corrections in the edge length.

arXiv commentPublished version: 6+7 pages, 3+3 figures

References in corpus (34)

• Shot Noise in Mesoscopic Conductors
• Topological orders and Edge excitations in FQH states
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
• 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?
• Towards identification of a non-abelian state: observation of a quarter of electron charge at $\nu =5/2$ quantum Hall state
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Quantum limit of heat flow across a single electronic channel
• 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
• Semiclassical theory of shot noise in mesoscopic conductors
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Shot Noise in Anyonic Mach-Zehnder Interferometer
• Transport in a disordered $\nu =2/3$ fractional quantum Hall junction
• Melting of interference in the fractional quantum Hall effect: Appearance of neutral modes
• On the Interpretation of Thermal Conductance of the nu=5/2 Edge
• Contacts and Edge State Equilibration in the Fractional Quantum Hall Effect
• Incoherent transport on the $\nu =2/3$ quantum Hall edge
• Partial equilibration of integer and fractional edge channels in the thermal quantum Hall effect
• Synthesizing a Fractional v=2/3 State from Particle and Hole States
• Comment on S. H. Simon, Interpretation of thermal conductance of the $\nu =5/2$ edge, arXiv:1801.09687
• Noise on complex quantum Hall edges: Chiral anomaly and heat diffusion
• Phenomenological theory of heat transport in the fractional quantum Hall effect
• Non-Equilibrated Counter Propagating Edge Modes in the Fractional Quantum Hall Regime
• Robust integer and fractional helical modes in the quantum Hall effect
• Charge equilibration in integer and fractional quantum Hall edge channels in a generalized Hall-bar device
• Line junction in a quantum Hall system with two filling fractions
• Signatures of neutral quantum Hall modes in transport through low-density constrictions

Cited by in corpus (40)

• Fractional charge and fractional statistics in the quantum Hall effects
• Novel method distinguishing between competing topological orders
• Vanishing thermal equilibration for hole-conjugate fractional quantum Hall states in graphene
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale
• Observation of ballistic upstream modes at fractional quantum Hall edges of graphene
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Fractional Edge Reconstruction in Integer Quantum Hall Phases
• Heat equilibration of integer and fractional quantum Hall edge modes in graphene
• Conductance plateaus and shot noise in fractional quantum Hall point contacts
• Contacts, equilibration, and interactions in fractional quantum Hall edge transport
• Edge Probes of Topological Order
• Full Classification of Transport on an Equilibrated 5/2 Edge via Shot Noise
• Fractionalized conductivity and emergent self-duality near topological phase transitions
• Energy relaxation in edge modes in the quantum Hall effect
• Does delta-$T$ noise probe quantum statistics?
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Quantized charge fractionalization at quantum Hall Y junctions in the disorder-dominated regime
• Shot noise as a diagnostic in the $\nu =2/3$ fractional quantum Hall edge zoo
• Influence of channel mixing in fermionic Hong-Ou-Mandel experiments
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• Identifying the topological order of quantized half-filled Landau levels through their daughter states
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Paired fermions in strong magnetic fields and daughters of even-denominator Hall plateaus
• Identifying non-Abelian anyons with upstream noise
• Symmetry-related transport on a fractional quantum Hall edge
• Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States
• Plasmon modes of coupled quantum Hall edge channels in the presence of disorder-induced tunneling
• Electrical noise spectroscopy of magnons in a quantum Hall ferromagnet
• Role of scaling dimensions in generalized noises in fractional quantum Hall tunneling due to a temperature bias
• Transport Signatures of Fractional Quantum Hall Binding Transitions
• Experimentally Motivated Order of Length Scales Affect Shot Noise
• Landscapes of an out-of-equilibrium anyonic sea
• Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases
• Ballistic-to-diffusive transition in engineered counter-propagating quantum Hall channels
• Manifestation of edge-bulk incompatibility in fractional quantum Hall platform
• Dc Electrical Current Generated by Upstream Neutral Modes
• Elevated Hall Responses as Indicators of Edge Reconstruction
• Extracting the scaling dimension of quantum Hall quasiparticles from current correlations
• Shot noise signatures of candidate states for the fractional quantum Hall $\nu =12/5$ state