PDEA Seminar: Anisotropic quantum Hall droplets

Abstract:

I will discuss recent work on 2D droplets of non-interacting electrons in strong magnetic fields, confined by an anisotropic trapping potential. Using semiclassical methods, we obtain the one-particle energy spectrum and wave functions in the lowest Landau level by deriving and solving a transport equation inspired by standard WKB theory. This shows that energy eigenstates are localized on equipotentials of the trap, generalizing the rotational-symmetric situation for isotropic traps. From these microscopic first-principle considerations, we obtain explicit results for many-body observables for anisotropic quantum Hall droplets in the thermodynamic limit, including its microwave absorption spectrum which we demonstrate should allow to experimentally probe the anisotropy. In particular, we show that correlations along the droplet’s edge are long-ranged, in agreement with low-energy edge modes described by a free chiral conformal field theory in terms of the canonical angle variable of the trapping potential.

Based on joint work arXiv:2301.01726 with B. Oblak, B. Lapierre, J.-M. Stéphan, and B. Estienne.

This is a seminar in the PDEs and Applications seminar series