Effects of electron-electron and electron-phonon interactions in weakly disordered conductors and heterostructures

We investigate quantum corrections to the conductivity due to the interference of electron-electron (electron-phonon) scattering and elastic electron scattering from impurities and defects in weakly disordered conductors. The interference corrections are proportional to the Drude conductivity and have various temperature dependences. The electron-electron interaction results in a $T^2\ln T$ correction in bulk conductors. In a quasi-two-dimensional (quasi-2D) conductor, $d<\mathrm{}{L}_T{=v}_F/T$ $(d$ is the thickness, and $v_F$ is the Fermi velocity), with 3D electron spectrum ${(p}_{F}d>\mathrm{}1)$ this correction is linear in temperature and differs from that for 2D electrons [G. Zala et al., Phys. Rev. B 64, 214204 (2001)] by a numerical factor. In quasi-one-dimensional conductors with 3D and 2D electron spectra (a wire with radius $r<\mathrm{}{L}_T$ and a strip with width $b<\mathrm{}{L}_T),$ temperature-dependent corrections are proportional to $\ln T.\mathrm{}$ The value and sign of the corrections depend on the strength of the electron-electron interaction in the triplet channel. The electron interaction via exchange of virtual phonons gives the $T^2\ln T$ correction. In bulk semiconductors the interaction of electrons with thermal phonons via the screened deformation potential results in a $T^6$ term and via unscreened deformation potential leads to a $T^2$ term. For a two-dimensional electron gas in heterostructures, the screened deformation potential gives rise to a $T^4$ term and the unscreened deformation potential leads to a $T^2\ln T$ term. At low temperatures the interference of electron-electron and electron-impurity scattering dominates in the temperature-dependent conductivity. At higher temperatures the conductivity is determined by the electron-phonon-impurity interference, which prevails over pure electron-phonon scattering in a wide temperature range, which extends with increasing disorder.