Interaction-induced magnetoresistance in a two-dimensional electron gas

We study the interaction-induced quantum correction δσαβ 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 δσαβ 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.