Edge electrostatics revisited

Salman A., YÜCEL M. B. , Siddiki A.

PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, cilt.47, ss.229-236, 2013 (SCI İndekslerine Giren Dergi) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47
  • Basım Tarihi: 2013
  • Doi Numarası: 10.1016/j.physe.2012.10.035
  • Sayfa Sayıları: ss.229-236


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 Chldovskii 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. (C) 2012 Elsevier B.V. All rights reserved.