The contribution of the electron-electron interaction to conductivity is analyzed step by step starting from the high conductivity in gated GaAs/In x Ga 1Ϫx As/GaAs heterostructures with different starting disorders. We demonstrate that the diffusion theory works down to k F lӍ1.5Ϫ2, where k F is the Fermi quasimomentum and l is the mean free path. It is shown that the e-e interaction gives smaller contribution to the conductivity than the interference independent of the starting disorder, and its role rapidly decreases with decreasing k F l.Quantum corrections to the conductivity in disordered metals and doped semiconductors have been intensively studied since 1980. 1 Two mechanisms led to these corrections: ͑i͒ the interference of the electron waves propagating in opposite directions along closed paths; ͑ii͒ electronelectron (e-e) interaction. The interference decreases the conductivity and its role increases with decreasing temperature. Behavior of the e-e contribution to the conductivity strongly depends on value of k B T/ប, where is transport relaxation time, and Fermi liquid interaction parameter F 0 . 2,3 It dramatically changes at crossover from the diffusion regime (k B T/បӶ1) to the ballistic one (k B T/បտ1) and can lead to inversion of sign of the temperature dependence of the conductivity. In addition, in the ballistic regime the e-e contribution depends on scale of scattering potential. The interaction correction for pointlike scattering potential was considered in Refs. 2 and 3 and for the long-range potential was studied theoretically in Ref. 4 and experimentally in Ref. 5. In this paper we track the evolution of the interaction correction as the conductivity decreases. Because the absolute value of both interference and interaction corrections increases with decreasing temperature, they determine in large part the low-temperature transport in two-dimensional ͑2D͒ systems in this case. The interference or weaklocalization ͑WL͒ correction ␦ WL is proportional to Ϫln( /), where is the phase relaxation time, ϰT Ϫp , pӍ1 in dirty limit. The correction due to the e-e interaction ␦ ee is proportional to Ϫln͓ប/(k B T)͔ in the diffusion regime. 1 It immediately follows that at increasing disorder, i.e., at decreasing , both corrections have to be enhanced in absolute value and can become comparable with the Drude conductivity. In this case the low-temperature conductivity will be significantly less than the Drude conductivity, and the strong temperature dependence of the conductivity has to appear. On further increase of disorder the transition to the hopping conductivity has to occur.All theories of quantum corrections for both diffusive 1 and ballistic 2-4 regimes were developed for the case k F l ӷ1, where k F and l are the Fermi quasimomentum and the classical mean free path, respectively. Under this condition the quantum corrections to the conductivity are small in magnitude compared with the Drude conductivity 0 ϭk F lG 0 with G 0 ϭe 2 /(2 2 ប) at any accessible temperature. With decreasing k F l ...

Statistics of closed paths in two-dimensional (2D) systems, which just determines the interference quantum correction to conductivity and anomalous magnetoconductance, has been studied by computer simulation of a particle motion over the plane with randomly distributed scatterers. Both ballistic and diffusion regimes have been considered. The results of simulation have been analyzed in the framework of diffusion approximation. They are used for calculation of the magnetic field dependence of magnetoconductance in the model 2D system. It is shown that the anomalous magnetoconductance can be in principle described by the well known expression, obtained in the diffusion approximation, but with the prefactor less than unity and phase breaking length which differs from true value.

Weak antilocalization is studied in an InGaAs quantum well. Anomalous magnetoresistance is measured and described theoretically in fields perpendicular, tilted and parallel to the quantum well plane. Spin and phase relaxation times are found as functions of temperature and parallel field. It is demonstrated that spin dephasing is due to the Dresselhaus spin-orbit interaction. The values of electron spin splittings and spin relaxation times are found in the wide range of 2D density. Application of in-plane field is shown to destroy weak antilocalization due to competition of Zeeman and microroughness effects. Their relative contributions are separated, and the values of the in-plane electron g-factor and characteristic size of interface imperfections are found.Comment: 8 pages, 8 figure

Results of detailed investigations of the conductivity and Hall effect in gated single quantum well GaAs/InGaAs/GaAs heterostructures with two-dimensional electron gas are presented. A successive analysis of the data has shown that the conductivity is diffusive for kF l = 25 − 2. The absolute value of the quantum corrections for kF l = 2 at low temperature is not small, e.g., it is about 70 % of the Drude conductivity at T = 0.46 K. For kF l = 2 − 0.5 the conductivity looks like diffusive one. The temperature and magnetic field dependences are qualitatively described within the framework of the self-consistent theory by Vollhardt and Wölfle. The interference correction is therewith close in magnitude to the Drude conductivity so that the conductivity σ becomes significantly less than e 2 /h. We conclude that the temperature and magnetic field dependences of conductivity in the whole kF l range are due to changes of quantum corrections.

We study, both theoretically and experimentally, the negative magnetoresistance (MR) of a twodimensional (2D) electron gas in a weak transverse magnetic field B. The analysis is carried out in a wide range of zero-B conductances g (measured in units of e 2 /h), including the range of intermediate conductances, g ∼ 1. Interpretation of the experimental results obtained for a 2D electron gas in GaAs/InxGa1−xAs/GaAs single quantum well structures is based on the theory which takes into account terms of higher orders in 1/g. We show that the standard weak localization (WL) theory is adequate for g 5. Calculating the corrections of second order in 1/g to the MR, stemming from both the interference contribution and the mutual effect of WL and Coulomb interaction, we expand the range of a quantitative agreement between the theory and experiment down to significantly lower conductances g ∼ 1. We demonstrate that at intermediate conductances the negative MR is described by the standard WL "digamma-functions" expression, but with a reduced prefactor α. We also show that at not very high g the second-loop corrections dominate over the contribution of the interaction in the Cooper channel, and therefore appear to be the main source of the lowering of the prefactor, α ≃ 1 − 2/πg. The fitting of the MR allows us to measure the true value of the phase breaking time within a wide conductance range, g 1. We further analyze the regime of a "weak insulator", when the zero-B conductance is low g(B = 0) < 1 due to the localization at low temperature, whereas the Drude conductance is high, g0 ≫ 1, so that a weak magnetic field delocalizes electronic states. In this regime, while the MR still can be fitted by the digamma-functions formula, the experimentally obtained value of the dephasing rate has nothing to do with the true one. The corresponding fitting parameter in the low-T limit is determined by the localization length and may therefore saturate at T → 0, even though the true dephasing rate vanishes.