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arXiv:cond-mat/0604387 · Journal of the Physical Society of Japan

Quantum Critical “Opalescence” around Metal–Insulator Transitions

Takahiro Misawa, Youhei Yamaji, Masatoshi Imada

Published Aug 10, 2006• 25 citations
arXivHTMLPDF

Abstract

Divergent carrier-density fluctuations equivalent to the critical opalescence of gas-liquid transitions emerge around a metal-insulator critical point at a finite temperature. In contrast to the gas-liquid transitions, however, the critical temperature can be lowered to zero, which offers a challenging quantum phase transition. We present a microscopic description of such quantum critical phenomena in two dimensions. The conventional scheme of phase transitions by Ginzburg, Landau and Wilson is violated and an unconventional universality appears. It offers a clear insight into the criticalities of metal-insulator transitions associated with Mott or charge-order transitions. Fermi degeneracy involving the diverging density fluctuations generates emergent phenomena near the endpoint of the first-order transition and must shed new light on remarkable phenomena found in correlated metals like unconventional cuprate superconductors. It indeed accounts for otherwise puzzling criticality of the Mott transition recently discovered in an organic conductor. We propose to measure enhanced dielectric fluctuations at small wavenumbers by accurate probes.

DOI
10.1143/jpsj.75.083705

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Divergent carrier-density fluctuations equivalent to the critical opalescence of gas-liquid transitions emerge around a metal-insulator critical point at a finite temperature. In contrast to the gas-liquid transitions, however, the critical temperature can be lowered to zero, which offers a challenging quantum phase transition. We present a microscopic description of such quantum critical phenomena in two dimensions. The conventional scheme of phase transitions by Ginzburg, Landau and Wilson is violated and an unconventional universality appears. It offers a clear insight into the criticalities of metal-insulator transitions associated with Mott or charge-order transitions. Fermi degeneracy involving the diverging density fluctuations generates emergent phenomena near the endpoint of the first-order transition and must shed new light on remarkable phenomena found in correlated metals like unconventional cuprate superconductors. It indeed accounts for otherwise puzzling criticality of the Mott transition recently discovered in an organic conductor. We propose to measure enhanced dielectric fluctuations at small wavenumbers by accurate probes.
Quantum criticality of metal-insulator transitions in correlated electron systems is shown to belong to an unconventional universality class with violation of the Ginzburg-Landau-Wilson (GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square lattices are capable of such metal-insulator transitions with unusual criticality under a preexisting symmetry breaking. The obtained universality is consistent with the scaling theory formulated for Mott transitions and with a number of numerical results beyond the mean-field level, implying that preexisting symmetry breaking is not necessarily required for the emergence of this unconventional universality. Examinations of fluctuation effects indicate that the obtained critical exponents remain essentially exact beyond the mean-field level. It further clarifies the whole structure of singularities by a unified treatment of the bandwidth-control and filling-control transitions. Detailed analyses of the criticality, containing diverging carrier density fluctuations around the marginal quantum critical point, are presented from microscopic calculations and reveal the nature as quantum critical ``opalescence.'' The mechanism of emerging marginal quantum critical point is ascribed to a positive feedback and interplay between the preexisting gap formation present even in metals and kinetic energy gain (loss) of the metallic carrier. Analyses of crossovers between GLW type at nonzero temperature and topological type at zero temperature show that the critical exponents observed in (V,Cr)2O3{(\mathrm{V},\mathrm{Cr})}_{2}{\mathrm{O}}_{3}(V,Cr)2​O3​ and $\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{ET}$-type organic conductors provide us with evidence for the existence of the present marginal quantum criticality.
The Mott critical point between a metal and a correlated insulator has usually been studied via density or spin density bosonic mode fluctuations according to the standard Ginzburg-Landau-Wilson phase transition paradigm. A moment's reflection leads to increasing doubts that such an approach should work as the transition is nonmagnetic, voiding the relevance of spin density modes. Charge density modes are irrelevelant since the long range Coulomb interaction leads to a large plasmon gap and their incompressibility. In solidarity with these doubts, recent measurements of the Mott critical point in low dimensional organic materials yield critical exponents in violent diasagreement with the bosonic mode criticality lore. We propose that fermionic fluctuations control the behavior of the Mott transition. The transition thus has an intrinsic quantum aspect despite being a finite temperature phase transition. We develop this hitherto unexplored physics, obtain experimental predictions and find agreement with one of the novel unexplained experimental exponents. We conclude that this Mott transition corresponds to a new universality class of finite temperature critical points that contains quantum effects and cannot be accounted for by conventional Ginzburg-Landau-Wilson wisdom.
The gas-liquid transition is a first-order transition terminating at a finite-temperature critical point with diverging density fluctuations. Mott transition, a metal-insulator transition driven by Coulomb repulsion between electrons, has been identified with this textbook transition. However, the critical temperature of the Mott transition can be suppressed, resulting in unusual quantum criticality. It accounts for non-Fermi-liquid-like properties, and strongly momentum dependent quasiparticles as in many materials near the Mott insulator. Among all, the mode-coupling theory of the density fluctuations supports d-wave superconductivity at the order of a hundred Kelvin for relevant parameters of the copper oxide superconductors.
Phenomenological theory of the Mott transition is presented. When the critical temperature of the Mott transition is much higher than the quantum degeneracy temperature, the transition is essentially described by the Ising universality class. Below the critical temperature, phase separation or first-order transition occurs. However, if the critical point is involved in the Fermi degeneracy region, a marginal quantum critical point appears at zero temperature. The originally single Mott critical point generates subsequent many unstable fixed points through various Fermi surface instabilities induced by the Mott criticality characterized by the diverging charge susceptibility or doublon susceptibility. This occurs in marginal quantum-critical region. Charge, magnetic and superconducting instabilitites compete severely under these critical charge fluctuations. The quantum Mott transition triggers multi-furcating criticality, which goes beyond the conventional concept of multicriticality in quantum phase transitions. Near the quantum Mott transition, the criticality generically drives growth of inhomogeneous structure in the momentum space with singular points of flat dispersion on the Fermi surface. The singular points determine the quantum dynamics of the Mott transition by the dynamical exponent z=4z=4z=4. We argue that many of filling-control Mott transitions are classified to this category. Recent numerical results as well as experimental results on strongly correlated systems including transition metal oxides, organic materials and 3^33He layer adsorbed on a substrate are consistently analyzed especially in two-dimensional systems.
The authors show that critical opalescence - enhanced density fluctuations at all length scales - occurs in quantum matter, specifically in a doped Mott-insulating system that can be realized with ultracold atoms in optical lattices. These findings provide a theoretical framework and new predictions for ultracold-atom experiments. Looking for critical opalescence across the doping-driven Mott transition in ultracold systems may give insights on the origin of the pseudogap in cuprate high-temperature superconductors.
Metallic states near the Mott insulator show a variety of quantum phases, including various magnetic, charge-ordered states and high-temperature superconductivity in various transition metal oxides and organic solids. The emergence of a variety of phases and their competitions are likely intimately associated with quantum transitions between the electron-correlation-driven Mott insulator and metals characterized by its criticality, and is related to many central questions of condensed matter. The quantum criticality is, however, not well understood when the transition is controlled by the bandwidth through physical parameters such as pressure. Here, we quantitatively estimate the universality class of the transition characterized by a comprehensive set of critical exponents by using a variational Monte Carlo method implemented as an open-source innovated quantum many-body solver, with the help of established scaling laws at a typical bandwidth-controlled Mott transition. The criticality indicates a weaker charge and density instability in contrast to the filling-controlled transition realized by carrier doping, implying a weaker instability to superconductivity as well. The present comprehensive clarification opens up a number of routes for quantitative experimental studies for complete understanding of elusive quantum Mott transition and nearby strange metal that cultivate future design of functionality.