Self-consistent calculations of edge channels in laterally confined two-dimensional electron systems.

Abstract

We calculate the distribution of incompressible and compressible regions at an electrostatically defined edge of a two-dimensional electron system (2DES) in a strong perpendicular magnetic field B for two models, one with a strictly 2D arrangement of gate and charges, and one with a realistic 3D structure. We ensure electrochemical equilibrium by self-consistent calculation of the electrostatic potential from the electron density and the boundary conditions defined by the metallic gates, and of the electron density in this potential, using the Thomas-Fermi approximation. Both models yield qualitatively the same results. In the limit of zero temperature and strong magnetic field, and at distances from the edge which are much larger than the effective Bohr radius, our 2D model yields quantitatively the same result for the density profile in the 2DES as recent work by Chklovskii, Shklovskii, and Glazman, who considered a purely electrostatic model, without requiring electrochemical equilibrium for B=0. We demonstrate explicitly how the incompressible regions are destroyed with increasing temperature.