Two-sites quantum island in the quasi-ballistic regime

TL;DR

This paper models a two-island quantum device in the integer quantum Hall regime, revealing its quantum critical behavior, universal conductance and noise characteristics, and predicting fractional charges for finite bias conditions.

Contribution

It maps the two-island quantum Hall device to the boundary sine-Gordon model, providing new insights into its quantum critical point and fractional charge predictions.

Findings

Mapping to boundary sine-Gordon model explains critical behavior

Universal conductance and noise expressions match experiments

Finite bias predicts fractional charge e/3 and generalization to e/(N+1)

Abstract

Quantum Hall edge channels can be combined with metallic regions to fractionalize electrons and form correlated impurity models. We study a minimal device, that has been experimentally achieved quite recently, with two floating islands connected to three edge channels via quantum point contacts in the integer quantum Hall regime. At high transparency of the quantum point contacts, we establish a mapping to the boundary sine-Gordon model and thereby reveal the nature of the quantum critical point. We deduce from this mapping universal expressions for the conductance and noise, in agreement with the experimental findings, and discuss the competition between Kondo-like screening of each individual island and the cooperative transfer of electrons between them. We further predict that the device operated at finite voltage bias produces fractional charges $e^* =e/3$ and propose a generalization to $N$ islands with the fractional charge $e^* =e/(N+1)$.