Metal-insulator transition in the compensated sodium bronze, ${\mathrm{Na}}_{\mathrm{x}}$${\mathrm{Ta}}_{\mathrm{y}}$${\mathrm{W}}_{1\mathrm{-}\mathrm{y}}$${\mathrm{O}}_3$

We have measured the dc electrical conductivity σ of cubic ${\mathrm{Na}}_{\mathrm{x}}$ ${\mathrm{Ta}}_{\mathrm{y}}$ ${\mathrm{W}}_{1\mathrm{-}\mathrm{y}}$ ${\mathrm{O}}_3$ from 1.6 to 295 K for various values of x and y. A sample with x-y=0.18 appears to fall directly at the metal-insulator transition and shows an unusual temperature dependence, σ(T)∝T, from 1.6 K to room temperature. A model for σ(T) based on the scaling theory of localization, when used to interpret the data on this and other samples, gives a conductivity exponent ν of 1.0. This model assumes that σ(T) is controlled by a thermal smearing of the occupancy of one-electron energy states near the Fermi level rather than by inelastic scattering. Comparison of the conductivity transition in ${\mathrm{Na}}_{\mathrm{x}}$ ${\mathrm{Ta}}_{\mathrm{y}}$ ${\mathrm{W}}_{1\mathrm{-}\mathrm{y}}$ ${\mathrm{O}}_3$ with earlier data for the uncompensated material ${\mathrm{Na}}_{\mathrm{x}}$ ${\mathrm{WO}}_3$ indicates that the additional disorder introduced by Ta doping does not shift the critical value of electron concentration.