Interaction corrections at intermediate temperatures: Longitudinal conductivity and kinetic equation

It is well known that electron-electron interaction in two-dimensional disordered systems leads to logarithmically divergent Altshuler-Aronov corrections to conductivity at low temperatures $(T\tau \ll 1;$ $\tau$ is the elastic mean-free time). This paper is devoted to the fate of such corrections at intermediate temperatures $T\tau \gtrsim 1.$ We show that in this (ballistic) regime the temperature dependence of conductivity is still governed by the same physical processes as the Altshuler-Aronov corrections—electron scattering by Friedel oscillations. However, in this regime the correction is linear in temperature; the value and even the sign of the slope depends on the strength of electron-electron interaction. (This sign change may be relevant for the “metal-insulator” transition observed recently.) We show that the slope is directly related to the renormalization of the spin susceptibility and grows as the system approaches the ferromagnetic Stoner instability. Also, we obtain the temperature dependence of the conductivity in the cross-over region between the diffusive and ballistic regimes. Finally, we derive the quantum kinetic equation, which describes electron transport for arbitrary value of $T\tau .$