Charging energy effects on a single-edge anyon braiding detector

TL;DR

This paper studies how capacitive coupling affects the detection of anyon braiding in a fractional quantum Hall interferometer, revealing the importance of accounting for charging energy to accurately measure the universal statistical angle.

Contribution

It introduces a Green's function formalism including charging energy to analyze capacitive effects on anyon braiding detection in a single-edge interferometer.

Findings

Capacitive effects modify current and cross-correlations in the device.

Charging energy influences the extraction of the statistical angle.

Measuring loop capacitance is essential for accurate braiding statistics.

Abstract

We investigate the influence of capacitive coupling on the detection of anyon braiding in a single-edge interferometer realized in the fractional quantum Hall regime. In this setup, a quantum point contact bends a single edge into a loop, where tunneling occurs at the open end and is controlled by the QPC voltage. In contrast with previously studied two-edge geometries, the weak backscattering regime is dominated by the first-order perturbative term, allowing quantum transport quantities to factorize into a non-universal prefactor and a braiding-induced contribution that provides direct access to the universal statistical angle $\pi\lambda$. While previous analyses neglected edge-to-edge capacitance, we show that capacitive effects, which are known to play a crucial role in mesoscopic capacitors, modify both the current and the current cross-correlations. Using a two-point Green's function formalism augmented by Dyson's equation to include the charging energy, we quantify how the fluctuations of the cross-correlations depend simultaneously on $\lambda$ and on the capacitance of the loop. Our results indicate that a reliable extraction of the statistical angle requires a parallel measurement of the loop capacitance, which can be implemented via a charged gate coupled to the junction.