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.
Highlights
The edge of quantum Hall (QH) phases supports gapless excitations. These are responsible for low-energy dynamics in such systems, including electrical and thermal transport and noise
This evokes questions of much broader scope: What is the interplay of topology and emergent symmetry, and what is its role in dictating transport and noise at the edge? To address these questions, we focus here on a paradigmatic example, that of a reconstructed and renormalized edge of the ν = 2/3 fractional quantum Hall (FQH) phase
This paper demonstrates that given the topological invariants of the bulk phase, different symmetries of the edge modes may underlie qualitatively different transport behavior, the dc conductance and the low-frequency nonequilibrium noise
Summary
The edge of quantum Hall (QH) phases supports gapless excitations. These are responsible for low-energy dynamics in such systems, including electrical and thermal transport and noise. A convenient working framework to study this physics is to describe the edge in terms of one-dimensional chiral Luttinger modes [1] This simple picture has proven more complex and exotic than first anticipated, especially in the context of fractional quantum Hall (FQH) phases [2,3,4,5,6,7,8,9,10,11,12,13,14,15]. The Kane-Fisher-Polchinski model [28] serves as an example of an emergent symmetry [SU(2)] due to a renormalization group (RG) of edge modes This evokes questions of much broader scope: What is the interplay of topology and emergent symmetry, and what is its role in dictating transport and noise at the edge? Our study may motivate the search for various symmetry scenarios with new experimental manifestations
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