Scaling tunnelling noise in the fractional quantum Hall effect tells about renormalization and breakdown of chiral Luttinger liquid

TL;DR

This study investigates tunnelling noise in fractional quantum Hall edges at filling factor 1/3, revealing renormalization of scaling dimensions and evidence of chiral Luttinger liquid breakdown at intermediate energies through novel scaling analysis.

Contribution

It provides the first quantitative analysis of CLL breakdown and renormalization of scaling dimensions using experimental tunnelling data at various temperatures.

Findings

Evidence of chiral Luttinger liquid breakdown above a certain energy scale.

Heavy renormalization of the scaling dimension compared to naive CLL predictions.

New insights into quantum Hall edge physics from reinterpreted older experiments.

Abstract

The fractional quantum Hall (FQH) effect provides a paradigmatic example of a topological phase of matter. FQH edges are theoretically described via models belonging to the class of chiral Luttinger liquid (CLL) theories [1 (Wen, 2007)]. These theories predict exotic properties of the excitations, such as fractional charge and fractional statistics. Despite theoretical confidence in this description and qualitative experimental confirmations, quantitative experimental evidence for CLL behaviour is scarce. In this work, we study tunnelling between edge modes in the quantum Hall regime at the filling factor $\nu=1/3$. We present measurements at different system temperatures and perform a novel scaling analysis of the experimental data, originally proposed in Ref. [2 (Schiller et al., 2022)]. Our analysis shows clear evidence of CLL breakdown - above a certain energy scale. In the low-energy regime, where the scaling behaviour holds, we extract the property called the scaling dimension and find it heavily renormalized compared to na\"ive CLL theory predictions. Our results show that decades-old experiments contain a lot of previously overlooked information that can be used to investigate the physics of quantum Hall edges. In particular, we open a road to quantitative experimental studies of (a) scaling dimension renormalization in quantum point contacts and (b) CLL breakdown mechanisms at an intermediate energy scale, much smaller than the bulk gap.