Per Moosavi: 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. 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.