Probing the $\nu=2/3$ fractional quantum Hall edge by momentum-resolved tunneling

TL;DR

This paper proposes an experimental approach using momentum-resolved tunneling between layered quantum Hall systems to investigate the edge modes of the $ u=2/3$ fractional quantum Hall state, considering interactions and disorder.

Contribution

It introduces a novel tunneling setup to probe the spectral function and edge mode nature of the $ u=2/3$ fractional quantum Hall state.

Findings

Threshold behavior reveals edge mode characteristics

Spectral function insights into chiral edge modes

Effects of Coulomb interaction and disorder analyzed

Abstract

The nature of the fractional quantum Hall state with filling factor $\nu=2/3$ and its edge modes continues to remain an open problem in low-dimensional condensed matter physics. Here, we suggest an experimental setting to probe the $\nu=2/3$ edge by tunnel-coupling it to a $\nu=1$ integer quantum Hall edge in another layer of a two-dimensional electron gas (2DEG). In this double-layer geometry, the momentum of tunneling electrons may be boosted by an auxiliary magnetic field parallel to the two planes of 2DEGs. We evaluate the current as a function of bias voltage and the boosting magnetic field. Its threshold behavior yields information about the spectral function of the $\nu=2/3$ edge, in particular about the nature of the chiral edge modes. Our theory accounts also for the effects of Coulomb interaction and disorder.