Broken Symmetries in the Reconstruction of ν = 1 Quantum Hall Edges

Spin-polarized reconstruction of the ν = 1 quantum Hall edge is accompanied by a spatial modulation of the charge density along the edge. We find that this is also the case for finite quantum Hall droplets: current spin density functional calculations show that the so-called Chamon-Wen edge forms a ring of apparently localized electrons around the maximum density droplet (MDD). The boundaries of these different phases qualitatively agree with recent experiments. For very soft confinement, Chern-Simons Ginzburg-Landau theory indicates formation of a non-translational invariant edge with vortices (holes) trapped in the edge region. Introduction Edge states in the quantum Hall regime have been subject to extensive study in recent years. In particular, much interest has focused on how the edge may reconstruct as the confining potential strength is varied (see [1] and Refs. therein). Various theoretical approaches, including Hartree-Fock methods, density functional theory, composite fermion models and effective (mean field) theories have been used to examine both small electron droplets (quantum dots) and large quantum Hall systems, with and without spin. In particular , many authors have been interested in edge reconstruction of ferromagnetic quantum Hall states, including ν = 1 and simple fractional (Laughlin) fillings. Softening of the confining edge potential allows charge to move outward, and the edge may reconstruct. How this happens, and whether or not the reconstruction involves spin textures, depends on the relative strength of the electron-electron interactions and the Zeeman energy, and on the steepness of the confining potential. Much work has been based on Hartee-Fock techniques. In 1994, Chamon and Wen found that the sharp ν = 1 edge of large systems or quantum dots may undergo a polarized reconstruction to a " stripe phase " [2], in which a lump of electrons becomes separated at a distance ∼ 2l B away from the original edge (l B =