Edge electrostatics revisited
PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES, cilt.47, ss.229-236, 2013 (SCI-Expanded)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 47
- Basım Tarihi: 2013
- Doi Numarası: 10.1016/j.physe.2012.10.035
- Dergi Adı: PHYSICA E-LOW-DIMENSIONAL SYSTEMS & NANOSTRUCTURES
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED)
- Sayfa Sayıları: ss.229-236
- Akdeniz Üniversitesi Adresli: Evet
Özet
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.