One of the striking predictions of quantum Hall edge theory, alongside the fractional charge and fractional statistics of the quasiparticles, is the power-law dependence of the conductance of a tunnel contact. This power-law dependence is characteristic of Luttinger liquids and is tied to the quasiparticle property called “scaling dimension”. Observing this behaviour is known to be problematic both in terms of achieving the qualitatively correct behaviour in experiments and quantitatively matching with theory [1–3].

I will present recent theory [4] that enables extracting the scaling dimension from the Fano factor – building upon the scheme long used to extract the fractional charge. I will further present the analysis of experimental data within this theoretical framework. I will demonstrate how it sheds light on the physics of quantum point contacts in the quantum Hall effect and opens new avenues to investigate renormalization of the Luttinger liquid behaviour.

[1] M. Heiblum, Quantum Shot Noise in Edge Channels, Phys. Status Solidi 243, 3604 (2006).
[2] I. P. Radu, J. B. Miller, C. M. Marcus, M. A. Kastner, L. N. Pfeiffer, and K. W. West, Quasi-Particle Properties from Tunneling in the $\nu = 5/2$ Fractional Quantum Hall State, Science 320, 899 (2008).
[3] S. Baer, C. Rössler, T. Ihn, K. Ensslin, C. Reichl, and W. Wegscheider, Experimental Probe of Topological Orders and Edge Excitations in the Second Landau Level, Phys. Rev. B 90, 075403 (2014).
[4] N. Schiller, Y. Oreg, and K. Snizhko, Extracting the Scaling Dimension of Quantum Hall Quasiparticles from Current Correlations, Phys. Rev. B 105, 165150 (2022).