Edge electrostatics revisited

In this work we investigate in detail, the different regimes of the pioneering work of Chklovskii et al. [1], which provides an analytical description to model the electrostatics at the edges of a two-dimensional electron gas. We take into account full electrostatics and calculate the charge distribution by solving the 3D Poisson equation self-consistently. The Chklovskii formalism is reintroduced and is employed to determine the widths of the incompressible edge-states also considering the spin degree of freedom. It is shown that, the odd integer filling fractions cannot exist for large magnetic field intervals if many-body effects are neglected. We explicitly show that, the incompressible strips which are narrower than the quantum mechanical length scales vanish. We numerically and analytically show that, the non-self-consistent picture becomes inadequate considering realistic Hall bar geometries, predicting large incompressible strips. The details of this picture are investigated considering device properties together with the many-body and the disorder effects. Moreover, we provide semi-empirical formulas to estimate realistic density distributions for different physical boundary conditions.

Graphical abstractIncompressible strip widths of ν=1ν=1 and ν=2ν=2 considering different Lande-g⁎ factors. The strip widths with black lines correspond to the Chklovskii formalism and red lines correspond to the self-consistent calculation.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► Edge electrostatics of two-dimensional electron gas is studied self-consistently. ► Width of incompressible edge states is obtained and compared with Chklovskii picture. ► We show that non-self-consistent picture fails for realistic Hall bar geometries. ► Non-self-consistent solution leads very wide incompressible strips. ► We derive semi-empirical formulas for electron density distributions and depletion lengths.