Two-sites quantum island in the quasi-ballistic regime

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 $e^{\ast }=e/3$ and propose a generalization to $N$ islands with the fractional charge $e^{\ast }=e/(N+1)$.

12 pages, 8 figures

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• Quantum criticality in coupled hybrid metal-semiconductor islands
• Systematic compactification of the two-channel Kondo model. II. Comparative study of scaling and universality
• Systematic compactification of the two-channel Kondo model. I. Consistent bosonization-debosonization approach and exact comparisons
• Multi-mode Coulomb blockade oscillations
• Breakdown of the Wiedemann-Franz law in an interacting quantum Hall metamaterial
• Tunneling in multi-site mesoscopic quantum Hall circuits