Size effects on electron-electron interactions in GaAs-AlxGa1−xAs heterostructures

Abstract

Magnetoresistance measurements are made on the two-dimensional (2D) electron gas in GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures to study the electron-electron interaction as a function of the sample width w. For w≳20 μm, the data fit the 2D interaction theory. For w<20 μm, the magnetoresistance shows a large enhancement for w≃3 μm, confirming the 2D-to-1D crossover expected from the interaction theory, and a drastic decrease for w≤2 μm, due to the increasing importance of boundary scattering.