Speaker
Description
The quantum Hall edge is conventionally described within the Luttinger liquid theory. This theory does not contain intrinsic energy scales, and thus predicts scale-invariant behaviour. This can be characterized via the quasiparticle property called “scaling dimension”.
Unlike the quasiparticle [fractional] charge and [fractional] statistics, the scaling dimension is not a fundamental property, but is a quantity that characterizes the quasiparticle dynamics. Nevertheless, the scale-invariant behaviour is the common property of all Luttinger-liquid models for quantum Hall edges.
Observing this behaviour is known to be problematic both in terms of achieving the qualitatively correct behaviour in experiments and quantitatively matching with theory [1], [2], [3] and has only been demonstrated in a limited number of experiments [4].
I will present recent theory [5] that enables model-independent verification of the scaling behaviour. I will further present the analysis of experimental data [6] within this theoretical framework. Our analysis clearly shows emergence of energy scales below the bulk gap that break the scaling behaviour. We further show that for small enough energies the scaling behaviour holds, yet the scaling dimension is heavily renormalized compared to naïve theory predictions.
This sheds light on the complex physics of quantum point contacts in the quantum Hall effect and opens up new avenues to investigate it.
Time permitting, I will comment on the recent results by Refs. [7], [8] that reported observing unrenormalized scaling dimension. In short, while the scaling dimension appears unrenormalized, the data of both works exhibit the scaling breakdown similar to the one we observe in Ref. [6].
[1] M. Heiblum, Quantum shot noise in edge channels, physica status solidi (b) 243, 3604 (2006), https://doi.org/10.1002/pssb.200642237.
[2] I. P. Radu et al., Quasi-Particle Properties from Tunneling in the $\nu = 5/2$ Fractional Quantum Hall State, Science 320, 899 (2008), https://doi.org/10.1126/science.1157560.
[3] S. Baer et al., Experimental probe of topological orders and edge excitations in the second Landau level, Phys. Rev. B 90, 075403 (2014), https://doi.org/10.1103/PhysRevB.90.075403.
[4] L. A. Cohen et al., Universal chiral Luttinger liquid behavior in a graphene fractional quantum Hall point contact, Science 382, 542 (2023), https://doi.org/10.1126/science.adf9728.
[5] N. Schiller, Y. Oreg, and K. Snizhko, Extracting the scaling dimension of quantum Hall quasiparticles from current correlations, Phys. Rev. B 105, 165150 (2022), https://doi.org/10.1103/PhysRevB.105.165150.
[6] N. Schiller et al., Scaling tunnelling noise in the fractional quantum Hall effect tells about renormalization and breakdown of chiral Luttinger liquid, https://arxiv.org/abs/2403.17097.
[7] A. Veillon et al., Observation of the scaling dimension of fractional quantum Hall anyons, Nature 632, 517 (2024), https://doi.org/10.1038/s41586-024-07727-z.
[8] R. Guerrero-Suarez et al., Universal Anyon Tunneling in a Chiral Luttinger Liquid, https://arxiv.org/abs/2502.20551.
