The metal-insulator transition in disordered 3d systems: a new view

The authors show that for an uncompensated semiconductor such as Si:P the metal-insulator transition occurs for -K F l>1 and the decrease of the conductivity sigma near the transition can be accounted for by perturbation theory. A universal dependence of sigma as a function of electron density n is given. sigma decreases with decreasing n due to formation of wavefunctions decaying with distance as a power law, causing a decrease of the diffusion constant. Electron correlation has only a small effect on sigma far above the metal-insulator transition. However, as n decreases and tends to n c , electron correlations cause a sharper decrease of sigma . For uncompensated samples transport is in a conduction band, the density of states deviates only slightly from a free-electron-like behaviour, whereas sigma drops below sigma B , the Boltzmann value of the conductivity, due to a reduction of the diffusion constant. A discontinuous transition to an impurity band occurs when the conductivity in the conduction band is about 0.03 sigma B and thus somewhat below Mott's value sigma min =0.03 e 2 /h(cross)a, which is correct for compensated samples. Conductivities much below sigma min for any sample must be due to long-range fluctuations or inhomogeneities. For uncompensated Si:P the authors argue for a minimum metallic conductivity of about 1 / 3 sigma min .