SOFT EDGES, RECONSTRUCTIONS, AND COLLECTIVE EDGE MODES OF THE 2-DIMENSIONAL WIGNER CRYSTAL

The structure of edge electrons in the magnetically induced Wigner crystal is examined in the situation of a soft-edge potential that allows the electron density to fall off slowly from its bulk value to zero. We find various reconstructions at the edges, which in many cases have structures that may be understood in terms of local charge neutrality. The collective modes for the system are computed using a classical method and it is found that there are very low-energy edge modes associated with the reconstructions. It is argued that a quantum treatment should lead to new gapless modes, since the reconstructions represent broken-symmetry states. In either case, it is expected that the existence of such low-energy modes implies that the edge electrons should be easily depinned from the bulk by a finite electric field. The effects of edge currents should play an important role in the conduction properties of narrow systems.