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Currents in the Compressible and Incompressible Regions of the 2DEG

Michael R. Geller·Giovanni Vignale
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Abstract

We derive a general expression for the low-temperature current distribution in a two-dimensional electron gas, subjected to a perpendicular magnetic field and in a confining potential that varies slowly on the scale of the magnetic length l. The analysis is based on a self-consistent one-electron description, such as the Hartree or standard Kohn-Sham equations. Our expression, which correctly describes the current distribution on scales larger than l, has two components: One is an ``edge current'' which is proportional to the local density gradient and the other is a ``bulk current'' which is proportional to the gradient of the confining potential. The direction of these currents generally displays a striking alternating pattern.

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Michael R. Geller, Giovanni Vignale. 1994-09-01. Currents in the Compressible and Incompressible Regions of the 2DEG. https://doi.org/10.1103/physrevb.50.11714

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