Determination of topological edge quantum numbers of fractional quantum Hall phases

Abstract

To determine the topological quantum numbers of fractional quantum Hall (FQH) states hosting counter-propagating (CP) downstream ($N_d$) and upstream ($N_u$) edge modes, it is pivotal to study quantized transport both in the presence and absence of edge mode equilibration. While reaching the non-equilibrated regime is challenging for charge transport, we target here the thermal Hall conductance $G_Q$, which is purely governed by edge quantum numbers $N_d$ and $N_u$. Our experimental setup is realized with a hBN encapsulated graphite gated monolayer graphene device. For temperatures up to $35mK$, our measured $G_Q$ at $\nu =$ 2/3 and 3/5 (with CP modes) match the quantized values of non-equilibrated regime $(N_d+N_u){\kappa }_{0}T$, where ${\kappa }_{0}T$ is a quanta of $G_Q$. With increasing temperature, $G_Q$ decreases and eventually takes the value of equilibrated regime $|N_d-N_u|{\kappa }_{0}T$. By contrast, at $\nu =$1/3 and 2/5 (without CP modes), $G_Q$ remains robustly quantized at $N_d{\kappa }_{0}T$ independent of the temperature. Thus, measuring the quantized values of $G_Q$ at two regimes, we determine the edge quantum numbers, which opens a new route for finding the topological order of exotic non-Abelian FQH states.

References in corpus (35)

• Topological orders and Edge excitations in FQH states
• Majorana quantization and half-integer thermal quantum Hall effect in a Kitaev spin liquid
• The hot pick-up technique for batch assembly of van der Waals heterostructures
• One-Dimensional Quantum Liquids: Beyond the Luttinger Liquid Paradigm
• Observation of half-integer thermal Hall conductance
• 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 a Luttinger liquid
• Reconstruction of Fractional Quantum Hall Edges
• Edge reconstruction in the fractional quantum Hall regime
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Decoherence and interactions in an electronic Mach-Zehnder interferometer
• Transport in a disordered $\nu =2/3$ fractional quantum Hall junction
• Incoherent transport on the $\nu =2/3$ quantum Hall edge
• Vanishing thermal equilibration for hole-conjugate fractional quantum Hall states in graphene
• 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
• Noise on the Non-Abelian $\nu =5/2$ Fractional Quantum Hall Edge
• Observation of ballistic upstream modes at fractional quantum Hall edges of graphene
• Absent thermal equilibration on fractional quantum Hall edges over macroscopic scale
• Partial Equilibration of the Anti-Pfaffian edge due to Majorana Disorder
• Partial equilibration of anti-Pfaffian edge modes at $\nu =5/2$
• Counter-propagating charge transport in the quantum Hall effect regime
• Fractional Edge Reconstruction in Integer Quantum Hall Phases
• Thermalization of acoustic excitations in a strongly interacting one-dimensional quantum liquid
• Contacts, equilibration, and interactions in fractional quantum Hall edge transport
• Realizing Universal Edge Properties in Graphene Fractional Quantum Hall Liquids
• Relaxation in Luttinger liquids: Bose-Fermi duality
• Kinetics of mobile impurities and correlation functions in one-dimensional superfluids at finite temperature
• Thermal equilibration on the edges of topological liquids
• Equilibration in a chiral Luttinger liquid
• Thermal transport and quench relaxation in nonlinear Luttinger liquids

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• 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
• Absence of heat flow in ν = 0 quantum Hall ferromagnet in bilayer graphene
• Vanishing bulk heat flow in the nu=0 quantum Hall ferromagnet in monolayer graphene
• Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States
• Localization and conductance in fractional quantum Hall edges
• 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
• Impact of potential and temperature fluctuations on charge and heat transport in quantum Hall edges in the heat Coulomb blockade regime
• The Monte Carlo simulation of the topological quantities in FQH systems
• Transport Signatures of Fractional Quantum Hall Binding Transitions
• Quantized Thermal Hall Conductance and the Topological Phase Diagram of a Superconducting Bismuth Bilayer
• Half-integer thermal conductance in the absence of Majorana mode
• Landscapes of an out-of-equilibrium anyonic sea
• Experimentally Motivated Order of Length Scales Affect Shot Noise
• Thermal Transport Imaging in the Quantum Hall Edge Channel
• Drag conductance induced by neutral-mode localization in fractional quantum Hall junctions
• Anisotropic Behavior of the Thermoelectric Power and the Thermal Conductivity in a Unidirectional Lateral Superlattice: A Typical Anisotropic System Exhibiting Two Distinct Nernst Coefficients
• Quantized heat flow in graphene quantum Hall phases: Probing the topological order
• Manifestation of edge-bulk incompatibility in fractional quantum Hall platform
• Composite fermions and parton wavefunctions in twisted graphene on hexagonal boron nitride
• Elevated Hall Responses as Indicators of Edge Reconstruction
• Shot noise signatures of candidate states for the fractional quantum Hall $\nu =12/5$ state