Incoherent transport on the $\nu =2/3$ quantum Hall edge

Abstract

The nature of edge state transport in quantum Hall systems has been studied intensely ever since Halperin [1] noted its importance for the quantization of the Hall conductance. Since then, there have been many developments in the study of edge states in the quantum Hall effect, including the prediction of multiple counter-propagating modes in the fractional quantum Hall regime, the prediction of edge mode renormalization due to disorder, and studies of how the sample confining potential affects the edge state structure (edge reconstruction), among others. In this paper, we study edge transport for the ${\nu }_{\text{bulk}}=2/3$ edge in the disordered, fully incoherent transport regime. To do so, we use a hydrodynamic approximation for the calculation of voltage and temperature profiles along the edge of the sample. Within this formalism, we study two different bare mode structures with tunneling: the original edge structure predicted by Wen [2] and MacDonald [3], and the more complicated edge structure proposed by Meir [4], whose renormalization and transport characteristics were discussed by Wang, Meir and Gefen (WMG) [5]. We find that in the fully incoherent regime, the topological characteristics of transport (quantized electrical and heat conductance) are intact, with finite size corrections which are determined by the extent of equilibration. In particular, our calculation of conductance for the WMG model in a double QPC geometry reproduce conductance results of a recent experiment by R. Sabo, et al. [17], which are inconsistent with the model of MacDonald. Our results can be explained in the charge/neutral mode picture, with incoherent analogues of the renormalization fixed points of Ref. [5]. Additionally, we find diffusive $(\sim 1/L)$ conductivity corrections to the heat conductance in the fully incoherent regime for both models of the edge.

40 pages, 10 figures. v2 added citations, now 41 pages

References in corpus (9)

• 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
• Observation of neutral modes in the fractional quantum Hall regime
• Extracting net current from an upstream neutral mode in the fractional quantum Hall regime
• Environmental induced renormalization effects in quantum Hall edge states
• Robust integer and fractional helical modes in the quantum Hall effect
• Line junction in a quantum Hall system with two filling fractions
• Transmission of heat modes across a potential barrier

Cited by in corpus (44)

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• Topological classification of shot noise on fractional quantum Hall edges
• Synthesizing a Fractional v=2/3 State from Particle and Hole States
• Anyons in Quantum Hall Interferometry
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Observation of ballistic upstream modes at fractional quantum Hall edges of graphene
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Noise on complex quantum Hall edges: Chiral anomaly and heat diffusion
• Determination of topological edge quantum numbers of fractional quantum Hall phases
• 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
• Phenomenological theory of heat transport in the fractional quantum Hall effect
• Andreev reflection of fractional quantum Hall quasiparticles
• Contacts, equilibration, and interactions in fractional quantum Hall edge transport
• Half-integer conductance plateau at the $\nu =2/3$ fractional quantum Hall state in a quantum point contact
• Quantized charge fractionalization at quantum Hall Y junctions in the disorder-dominated regime
• Charge equilibration in integer and fractional quantum Hall edge channels in a generalized Hall-bar device
• Thermal conductance and noise of Majorana modes along interfaced $\nu =5/2$ fractional quantum Hall states
• Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases
• Magnetic field dependent equilibration of fractional quantum Hall edge modes
• Coherent-Incoherent Crossover of Charge and Neutral Mode Transport as Evidence for the Disorder-Dominated Fractional Edge Phase
• Fingerprints of anti-Pfaffian topological order in quantum point contact transport
• 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
• Localization and conductance in fractional quantum Hall edges
• 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
• Temperature dependent equilibration of spin orthogonal quantum Hall edge modes
• 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
• Spin-polarized voltage probes for helical edge state: a model study
• Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions
• Exchange-phase erasure in anyonic Hong-Ou-Mandel interferometry
• Ballistic-to-diffusive transition in engineered counter-propagating quantum Hall channels
• Dc Electrical Current Generated by Upstream Neutral Modes
• Elevated Hall Responses as Indicators of Edge Reconstruction
• Collapse of edge reconstruction in compressible Quantum Hall fluid within filling fraction range 2/3 to 1
• Extracting the scaling dimension of quantum Hall quasiparticles from current correlations
• Symmetric localization of ${\nu }_{\text{tot}}=4/3$ fractional topological insulator edges