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, Tc, below which the first-order transition occurs. The quantum regime describes the Tc=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 a new 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.The obtained universality classes agree with the recent experimental results for organic conductors, kappa-(ET)2Cu[N(CN)2]Cl and transition metal compounds such as V2O3. The mode coupling theory shows that the marginal quantum criticality further generates non-Fermi-liquid properties in the metallic side. A mechanism of high temperature superconductivity emerges from the density fluctuations at small wavenumber. The mode coupling theory combined with the Eliashberg equation predicts the superconductivity of the d wave symmetry with the transition temperature of the correct order of magnitude for the realistic parameters for the cuprate superconductors. 
Masatoshi Imada