Detecting Non-Abelian Anyons by Charging Spectroscopy

TL;DR

This paper proposes a microscopic model to detect non-Abelian anyons in the fractional quantum Hall state through charge spectroscopy, predicting measurable signatures like slope changes and even-odd effects in stability diagrams.

Contribution

It introduces a detailed model linking non-Abelian statistics to charge stability diagrams, enabling experimental detection via temperature-dependent spectroscopy.

Findings

Predicts a measurable slope for the first quasiparticle charging line.

Identifies an even-odd effect as a signature of non-Abelian statistics.

Shows broadening effects at finite temperature in the charge stability diagram.

Abstract

Observation of non-Abelian statistics for the e/4 quasiparticles in the \nu=5/2 fractional quantum Hall state remains an outstanding experimental problem. The non-Abelian statistics are linked to the presence of additional low energy states in a system with localised quasiparticles, and hence an additional low-temperature entropy. Recent experiments, which detect changes in the number of quasiparticles trapped in a local potential well as a function of an applied gate voltage, V_G, provide a possibility for measuring this entropy, if carried out over a suitable range of temperatures, T. We present a microscopic model for quasiparticles in a potential well and study the effects of non-Abelian statistics on the charge stability diagram in the V_G-T plane, including broadening at finite temperature. We predict a measurable slope for the first quasiparticle charging line, and an even-odd effect in the diagram, which is a signature of non-Abelian statistics.