Boundary scattering and weak localization of electrons in a magnetic field

The influence of boundary scattering on one- and two-dimensional weak localization is studied both analytically and by numerical simulation. Diffuse and specular boundary scattering are considered for two geometries, a metal film in a parallel magnetic field and a laterally restricted two-dimensional electron gas in a perpendicular field. The results, which extend the Al’tshuler-Aronov and Dugaev-Khmel’nitskii theories, are relevant to recent magnetoresistance experiments on high-mobility channels in GaAs-${\mathrm{Al}}_{\mathrm{x}}$ ${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$As heterostructures.