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.

14 pages, 6 figures

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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