Interaction-induced magnetoresistance in a two-dimensional electron gas

We study the interaction-induced quantum correction δσ_αβ to the conductivity tensor of electrons in two dimensions for arbitrary Tτ (where T is the temperature and τ the transport scattering time), magnetic field, and type of disorder. A general theory is developed, allowing us to express δσ_αβ in terms of classical propagators (“ballistic diffusons”). The formalism is used to calculate the interaction contribution to the longitudinal and the Hall resistivities in a transverse magnetic field in the whole range of temperature from the diffusive (Tτ≪1) to the ballistic (Tτ≳1) regime, both in smooth disorder and in the presence of short-range scatterers. Further, we apply the formalism to anisotropic systems and demonstrate that the interaction induces quantum oscillations in the resistivity of lateral superlattices.