Magnetoresistance and dephasing in a two-dimensional electron gas at intermediate conductances

We study, both theoretically and experimentally, the negative magnetoresistance (MR) of a two-dimensional (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 e²∕h), including the range of intermediate conductances g~1. Interpretation of the experimental results obtained for a 2D electron gas in GaAs∕InₓGa_1-xAs∕GaAs single quantum well structures is based on a theory that takes into account terms of higher orders in $1∕g$. We show that the standard weak localization (WL) theory is adequate for g5. 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 α1-2∕πg. The fitting of the MR allows us to measure the true value of the phase breaking time within a wide conductance range g1. 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.