Metal-insulator transition: the Mott criterion and coherence length

On the basis of the Mott criterion for metal-insulator transition (MIT), an expression for the correlation length, identical to that for the coherence length in the theory of superconductivity, is obtained. This correlation length characterizes the size of an electron-hole pair (in an excitonic insulator) or the effective Bohr radius (as, e.g., in doped semiconductors). The relation obtained is used for calculation of the coherence length in vanadium dioxide. The presence of two characteristic coherence lengths (xi(1) similar to 20 Angstrom and xi(2) similar to 2 Angstrom) is found. This is associated with the specific features of the transition mechanism in VO2: this mechanism represents a combination of the purely electronic Mott-Hubbard contribution and the structural (Peierls-like) one. It is shown, however, that the driving force of the MIT in VO2 is the electron-correlation Mott-Hubbard transition.