2005/06/19 by Masatoshi Imada
Materials Science · Physics and Astronomy · #Organic and Molecular Conductors Research #Physics of Superconductivity and Magnetism #Quantum and electron transport phenomena #cond-mat.mtrl-sci #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.72.075113
published as Phys. Rev. B 72, 075113 (2005) · 47 pages including 8 figures
arxiv created 2005/06/19 · openalex publication_date 2005/08/08 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 an unusual universality class, where the order parameter exponent \ensuremathβ, the susceptibility exponent \ensuremathγ, and the field exponent \ensuremathδ are given by \ensuremathβ=d∕2, \ensuremathγ=2\ensuremath-d∕2, and \ensuremathδ=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 \ensuremathκ\text\ensuremath-(ET)2Cu[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_x2\ensuremath-y2 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.