Charge and current oscillations in fractional quantum Hall systems with edges

Abstract

Stationary solutions of the Chern-Simons effective field theory for the fractional quantum Hall systems with edges are presented for Hall bar, disk and annulus. In the infinitely long Hall bar geometry (non compact case), the charge density is shown to be monotonic inside the sample. In sharp contrast, spatial oscillatory modes of charge density are found for the two circular geometries, which indicate that in systems with compact geometry, charge and current exist also far from the edges.

Planar array of semiconducting nanotubes in an external electric field: Collective screening and polarizability

“…This step is well justified for a dense array. In the electrostatics of inhomogeneous fractional quantum Hall liquids 40,41 the charge distribution is described by the equations similar to Eq. ( 5), i.e., with logarithmic kernel, but with self-action playing an important role.…”