The effect of the frozen and pinned surface approximations on the spatial distribution of incompressible and compressible strips in quantum Hall regime

TL;DR

This study investigates how pinned and frozen surface boundary conditions influence the spatial distribution of compressible and incompressible strips in a quantum Hall regime using a semi-classical approach.

Contribution

It provides a comparative analysis of boundary condition effects on electron strip distributions in quantum Hall systems, highlighting their significant impact.

Findings

Boundary conditions significantly affect strip distributions.

Pinned and frozen surface approximations lead to different spatial profiles.

The semi-classical Thomas-Fermi method effectively models these effects.

Abstract

Pinned surface and frozen surface approximations are two commonly used approximations for the boundary conditions at the exposed surfaces of semiconductor structures. We have studied the effect of pinned surface and frozen surface boundary conditions on the spatial distribution of compressible and incompressible strips observed in the two dimensional electron gas formed in a GaAs/AlGaAs heterostructure under quantum Hall effect regime. We have used semi classical Thomas-Fermi method for describing the many body problem along with the Poisson equation for electrostatics. We observe that the boundary conditions significantly effect the spatial distributions of the compressible and incompressible strips.