Scaling tunnelling noise in the fractional quantum Hall effect tells about renormalization and breakdown of chiral Luttinger liquid
arxiv(2024)
摘要
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
ν=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 naïve 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.
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