Tunneling in multi-site mesoscopic quantum Hall circuits

TL;DR

The paper investigates transport in multi-site mesoscopic quantum Hall circuits, focusing on the four-site geometry where higher-order backscattering becomes relevant. By bosonizing the edge channels and integrating out gapped charge modes, it derives an effective low-energy Hamiltonian with competing boundary perturbations in a single gapless mode, revealing a tunable quantum-critical point that yields unit conductance at zero temperature. The work further generalizes to multichannel circuits, showing how looped edge channels can realize a family of non-Fermi-liquid exponents by reducing to a single effective mode, and discusses heating effects under bias. The findings provide a controllable platform to study quantum criticality, non-Fermi-liquid transport, and energy transfer in strongly correlated mesoscopic systems, with practical guidance for experiments via gate-tuning and channel looping.

Abstract

Transport properties of the single- and two-site mesoscoipc quantum Hall (QH) circuits at high transparencies can be described in terms of the lowest-order backscattering perturbations, and mapping to the boundary sine-Gordon model can be exploited in full generality. While the higher-order backscattering processes are exactly marginal in the case of corresponding three-site circuits, they become crucial in a device with four or more sites. Here, we explore the transport properties of a multi-site QH circuit with special focus on that with four sites, and report their unique quantum critical behaviors that can be accessed via transport measurements. Tunneling phenomena in multichannel QH circuits based on multi-site geometry are also investigated, and a promising route to realizing different aspects of quantum critical phenomena is offered

Figures (3)

• Figure 1: Schematic of the four-site quantum Hall circuit consisting of four essentially identical metallic islands connected by five external quantum point contacts (QPCs). Each island is connected to separate external gates (green metallic plates). The red dots represent the backscattering centers of fully-tunable QPCs. The right-moving edge state on the left is voltage $V$ biased, and charge current is measured at the QPC5. The symbol $\Phi_{\rm jR/L}$ stands for the bosonic field describing the right/left moving edge state.
• Figure 2: Schematics representation of the setup \ref{['fig1']} in asymmetric tunneling regime (see text for the details).
• Figure 3: (a) Typical realization of two-channel, two-site quantum Hall cricuits. (b) The setup (a) with one of the channels being looped. The red dot represents finite backscatterings, while in the case of the cross symbol, the corresponding QPC is fully opened. Notice that the gates are not explicitly shown (see text for the details).