Interaction-induced magnetoresistance in a two-dimensional electron gas

We study the interaction-induced quantum correction $\delta {\sigma }_{\alpha \beta }$ to the conductivity tensor of electrons in two dimensions for arbitrary $T\tau$ (where T is the temperature and $\tau$ the transport scattering time), magnetic field, and type of disorder. A general theory is developed, allowing us to express $\delta {\sigma }_{\alpha \beta }$ 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 $(T\tau \ll 1)$ to the ballistic $\left(T\tau \gtrsim 1\right)$ 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.