Experimental evidence for an inhomogeneous state of the correlated two-dimensional electron system in the vicinity of a metal–insulator transition

From measurements of the oscillatory magnetoresistance in weak perpendicular magnetic fields, we found that the quantum oscillations in two-dimensional electron systems in Si-MOS structures are observed down to the critical carrier density $n_c$ of the transition to the strongly localized state. For such low densities, the oscillations exhibit an anticipated period, phase, and amplitude, even though the conductivity becomes less than $e^2/h$, and, hence, the mean free path becomes less than the Fermi wavelength $\lambda_{\mathrm{F}}$. We believe that this apparent contradiction with the Ioffe-Regel criterion for diffusive transport is caused by emergence of an inhomogeneous state of the $\mathrm{2D}$ system, in which the regions of diffusive and hopping conduction are spatially separated.