Universality classes of metal-insulator transitions in strongly correlated electron systems and mechanism of high-temperature superconductivity

We study three regimes of the Mott transitions characterized by classical, marginally quantum, and quantum. In the classical regime, the quantum degeneracy temperature is lower than the critical temperature of the Mott transition T-c, below which the first-order transition occurs. The quantum regime describes the T-c=0 boundary of the continuous transition. The marginal quantum region appears sandwiched by these two regimes. The classical transition is described by the Ising universality class. However, the Ginzburg-Landau-Wilson scheme breaks down when the quantum effects dominate. The marginal quantum critical region is categorized to an unusual universality class, where the order parameter exponent beta, the susceptibility exponent gamma, and the field exponent delta are given by beta=d/2, gamma=2-d/2, and delta=4/d, respectively, with d being the spatial dimensionality. It is shown that the transition is always at the upper critical dimension irrespective of the spatial dimensions. Therefore the mean-field exponents and the hyperscaling description become both valid at any dimension. The obtained universality classes agree with the recent experimental results on the Mott criticality in organic conductors such as kappa-(ET)(2)Cu[N(CN)(2)]Cl and transition-metal compounds such as V2O3. The marginal quantum criticality is characterized by the critically enhanced electron-density fluctuations at small wave number. The characteristic energy scale of the density fluctuation extends to the order of the Mott gap in contrast to the spin and orbital fluctuation scales and causes various unusual properties. The mode coupling theory shows that the marginal quantum criticality further generates non-Fermi-liquid properties in the metallic side. The effects of the long-range Coulomb force in the filling-control Mott transition are also discussed. A mechanism of high-temperature superconductivity emerges from the density fluctuations at small wave number inherent in the marginal quantum criticality of the Mott transition. The mode coupling theory combined with the Eliashberg equation predicts the superconductivity of the d(x)(2)-y(2) symmetry with the transition temperature of the correct order of magnitude for the realistic parameters for the cuprate superconductors. Experimental results on the electron differentiations established in the angle-resolved photoemission experiments are favorably compared with the present prediction. The tendency for the spatial inhomogeneity is a natural consequence of this criticality.