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Giant suppression of the Drude conductivity due to quantum interference in disordered two-dimensional systems

Temperature and magnetic field dependences of the conductivity in heavily doped, strongly disordered two-dimensional quantum well structures GaAs/In$_x$Ga$_{1-x}$As/GaAs are investigated within wide conductivity and temperature ranges. Role of the interference in the electron transport is studied in the regimes when the phase breaking length $L_ϕ$ crosses over the localization length $ξ\sim l\exp{(πk_Fl/2)}$ with lowering temperature, where $k_F$ and $l$ are the Fermi quasimomentum and mean free path, respectively. It has been shown that all the experimental data can be understood within framework of simple model of the conductivity over delocalized states. This model differs from the conventional model of the weak localization developed for $k_Fl\gg 1$ and $L_ϕ\llξ$ by one point: the value of the quantum interference contribution to the conductivity is restricted not only by the phase breaking length $L_ϕ$ but by the localization length $ξ$ as well. We show that just the quantity $(τ_ϕ^\ast)^{-1}=τ_ϕ^{-1}+τ_ξ^{-1}$ rather than $τ_ϕ^{-1}$, where $τ_ϕ\propto T^{-1}$ is the dephasing time and $τ_ξ\simτ\exp(πk_F l)$, is responsible for the temperature and magnetic field dependences of the conductivity over the wide range of temperature and disorder strength down to the conductivity of order $10^{-2} e^2/h$.