Tunneling in multisite mesoscopic quantum Hall circuits
Phys. Rev. B 113, 155411 – Published 8 April, 2026
DOI: https://doi.org/10.1103/h3ws-zx8f
Abstract
Transport properties of single- and two-site mesoscopic quantum Hall (QH) circuits at high transparencies can be described in terms of the lowest-order backscattering processes, enabling a mapping to the boundary sine-Gordon model. We show that this description breaks down in circuits with four or more sites, where higher-order backscattering processes become relevant and qualitatively modify the low-energy physics, while remaining exactly marginal in three-site geometries. Focusing on the four-site circuit, we derive an effective low-energy theory that captures the resulting interaction-driven physics and reveals the emergence of unique quantum critical points. In the vicinity of these critical points, we obtain universal conductance and scaling behavior and establish the robustness of the associated non-Fermi liquid physics. We further introduce tunneling in multichannel multisite QH circuits and propose a promising route for realizing diverse quantum critical phenomena. We show that a boundary sine-Gordon description can be restored in multichannel multisite QH circuits by appropriately looping selected edge channels, a procedure that is experimentally feasible. Finally, we analyze the nonequilibrium heating effects relevant to transport measurements in QH circuits. Altogether, our results establish multisite QH circuits as a versatile and highly controllable platform for simulating interaction-driven quantum critical phenomena.
