Symmetry-related transport on a fractional quantum Hall edge

Abstract

Low-energy transport in quantum Hall states is carried through edge modes, and is dictated by bulk topological invariants and possibly microscopic Boltzmann kinetics at the edge. Here we show how the presence or breaking of symmetries of the edge Hamiltonian underlie transport properties, specifically d.c. conductance and noise. We demonstrate this through the analysis of hole-conjugate states of the quantum Hall effect, specifically the $\nu =2/3$ case in a quantum point-contact (QPC) geometry. We identify two symmetries, a continuous $SU(3)$ and a discrete $Z_3$, whose presence or absence (different symmetry scenarios) dictate qualitatively different types of behavior of conductance and shot noise. While recent measurements are consistent with one of these symmetry scenarios, others can be realized in future experiments.

arXiv comment14 pages, 6 figures

References in corpus (33)

• Sharp and Smooth Boundaries of Quantum Hall Liquids
• Quantized Thermal Transport in the Fractional Quantum Hall Effect
• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Observation of neutral modes in the fractional quantum Hall regime
• Impurity scattering and transport of fractional Quantum Hall edge state
• Local Thermometry of Neutral Modes on the Quantum Hall Edge
• Reconstruction of Fractional Quantum Hall Edges
• Bosonization of one dimensional fermions out of equilibrium
• Edge reconstruction in the fractional quantum Hall regime
• Edge reconstruction in the $\nu =2/3$ fractional quantum Hall state
• Proliferation of neutral modes in fractional quantum Hall states
• A New Paradigm for Edge Reconstruction in Fractional Quantum Hall States
• Field Theoretical Description of Quantum Hall Edge Reconstruction
• Current Correlations from a Mesoscopic Anyon Collider
• Composite Edge States in the $\nu =2/3$ Fractional Quantum Hall Regime
• Transport in a disordered $\nu =2/3$ fractional quantum Hall junction
• Energy relaxation at quantum Hall edge
• Chargeless heat transport in the fractional quantum Hall regime
• Melting of interference in the fractional quantum Hall effect: Appearance of neutral modes
• Incoherent transport on the $\nu =2/3$ quantum Hall edge
• Non-equilibrium Luttinger liquid: Zero-bias anomaly and dephasing
• Topological classification of shot noise on fractional quantum Hall edges
• Synthesizing a Fractional v=2/3 State from Particle and Hole States
• Extracting net current from an upstream neutral mode in the fractional quantum Hall regime
• Noise on complex quantum Hall edges: Chiral anomaly and heat diffusion
• Thermoelectric probe for neutral edge modes in the fractional quantum Hall regime
• Fractional Edge Reconstruction in Integer Quantum Hall Phases
• Conductance plateaus and shot noise in fractional quantum Hall point contacts
• Non-equilibrium noise in transport across a tunneling contact between $\nu =2/3$ fractional quantum Hall edges
• Neutral mode heat transport and fractional quantum Hall shot noise
• Signatures of neutral quantum Hall modes in transport through low-density constrictions
• Transmission of heat modes across a potential barrier
• Universal non-equilibrium states at the fractional quantum Hall edge

Cited by in corpus (9)

• Anyons in Quantum Hall Interferometry
• Does shot noise always provide the quasiparticle charge?
• Observation of the scaling dimension of fractional quantum Hall anyons
• Shot noise as a diagnostic in the $\nu =2/3$ fractional quantum Hall edge zoo
• Emergence of Neutral Modes in Laughlin-like Fractional Quantum Hall Phases
• Multiple Mechanisms for Emerging Conductance Plateaus in Fractional Quantum Hall States
• Experimentally Motivated Order of Length Scales Affect Shot Noise
• Edge Reconstruction and Emergent Neutral Modes in Integer and Fractional Quantum Hall Phases
• Manifestation of edge-bulk incompatibility in fractional quantum Hall platform