Observation of the scaling dimension of fractional quantum Hall anyons

TL;DR

This study measures the scaling dimension of fractional quantum Hall anyons by analyzing thermal and shot noise crossover, providing experimental confirmation of their theoretical properties across multiple conditions.

Contribution

It introduces a novel method to determine the scaling dimension from noise measurements, overcoming previous non-universal complications.

Findings

Measured scaling dimensions consistent with theory at multiple filling factors

Validated the noise crossover method as a robust probe of anyonic properties

Confirmed the central role of the scaling dimension in quasiparticle dynamics

Abstract

Unconventional quasiparticles emerging in the fractional quantum Hall regime present the challenge of observing their exotic properties unambiguously. Although the fractional charge of quasiparticles has been demonstrated since nearly three decades, the first convincing evidence of their anyonic quantum statistics has only recently been obtained and, so far, the so-called scaling dimension that determines the quasiparticles propagation dynamics remains elusive. In particular, while the non-linearity of the tunneling quasiparticle current should reveal their scaling dimension, the measurements fail to match theory, arguably because this observable is not robust to non-universal complications. Here we expose the scaling dimension from the thermal noise to shot noise crossover, and observe an agreement with expectations. Measurements are fitted to the predicted finite temperature expression involving both the quasiparticles scaling dimension and their charge, in contrast to previous charge investigations focusing on the high bias shot noise regime. A systematic analysis, repeated on multiple constrictions and experimental conditions, consistently matches the theoretical scaling dimensions for the fractional quasiparticles emerging at filling factors 1/3, 2/5 and 2/3. This establishes a central property of fractional quantum Hall anyons, and demonstrates a powerful and complementary window into exotic quasiparticles.