Sharp and smooth boundaries of quantum Hall liquids

We study the transition between sharp and smooth density distributions at the edges of quantum Hall liquids in the presence of interactions. We find that, for strong confining potentials, the edge of a ν=1 liquid is described by the ${\mathit{Z}}_{\mathit{F}}$=1 Fermi-liquid theory, even in the presence of interactions, a consequence of the chiral nature of the system. When the edge confining potential is decreased beyond a point, the edge undergoes a reconstruction and electrons start to deposit a distance ∼2 magnetic lengths away from the initial quantum Hall liquid. Within the Hartree-Fock approximation, a new pair of branches of gapless edge excitations is generated after the transition. We show that the transition is controlled by the balance between a long-ranged repulsive Hartree term and a short-ranged attractive exchange term. Such a transition also occurs for quantum dots in the quantum Hall regime and should be observable in resonant tunneling experiments. We find that the edge theory for sharp edges also applies to smooth edges (i.e., reconstructed edges) once the additional pairs of edge branches are included. Electron tunneling into the reconstructed edge is also discussed.