Edge of the two-dimensional electron gas in a gated heterostructure

Abstract
We describe a quantitative electrostatic theory of the two-dimensional electron gas (2DEG) confined by a semi-infinite gate. It includes the finite depth of the 2DEG below the surface of a heterostructure, which enables us to treat the whole range of gate voltages. Two models are used for the boundary condition on the free surface, with either pinned potential or frozen charge. Our results predict the position and width of the strips of incompressible liquid in the quantum Hall regime, and are in good agreement with recent experiments.

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