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 T² ln T correction in bulk conductors. In a quasi-two-dimensional (quasi-2D) conductor, d < L_T = v_F/T (d is the thickness, and v_F is the Fermi velocity), with 3D electron spectrum (p_Fd > 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 < L_T and a strip with width b < L_T), temperature-dependent corrections are proportional to ln T. 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 T² ln T correction. In bulk semiconductors the interaction of electrons with thermal phonons via the screened deformation potential results in a T⁶ term and via unscreened deformation potential leads to a T² term. For a two-dimensional electron gas in heterostructures, the screened deformation potential gives rise to a T⁴ term and the unscreened deformation potential leads to a T² 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.