Anisotropic Quantum Hall Droplets
Blagoje Oblak (ULB Brussels)
This talk is devoted to 2D droplets of noninteracting electrons in a strong magnetic field, placed in an arbitrary confining potential. I show that semiclassical methods in the lowest Landau level yield near-Gaussian energy eigenstates localized on level curves of the potential, implying explicit formulas for local many-body observables in the thermodynamic limit. In particular, correlations along a droplet’s edge are long-ranged, in accordance with the 1D chiral conformal field theory that describes its low-energy dynamics. This notably involves inhomogeneous correlations and position-dependent guiding centre velocities, but still results in a homogeneous theory thanks to remarkable cancellations between the radial and angular dependencies of eigenfunctions. Finally, I describe realistic microwave absorption experiments that probe the detailed shape of a droplet without resorting to local imaging.