Specific features of electrical conductivity of the insulating phase of vanadium dioxide doped with niobium

The electrical conductivity of V$_{1-x}$Nb$_{x}$O$_{2}$ single crystals have been investigated over a wide temperature range covering regions of the existence of the metallic and insulating phases. It has been shown that, with an increase in the niobium concentration, the electrical conductivity of the metallic phase becomes below the Mott limit for the minimum metallic conductivity. Immediately after the metal–insulator transition, the electrical conductivity is determined by a large amount of free electrons that gradually localized with a decrease in the temperature. The temperature dependence of the electrical conductivity in the insulating phase of V$_{1-x}$Nb$_{x}$O$_{2}$ has been explained in the framework of the hopping conductivity model that takes into account the effect of thermal vibrations of atoms on the resonance integral.