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Condensed Matter

Dynamic Correlations in Disordered Systems: Implications for High-Temperature Superconductivity

T. Egami

Published Feb 3, 2024• 1 citation
Publisher

Abstract

Liquid and gas are distinct in their extent of dynamic atomic correlations; in gas atoms are almost uncorrelated whereas they are strongly correlated in liquid. This distinction applies also to electronic systems. Fermi liquids are actually gas-like, whereas strongly correlated electrons are liquid-like. Doped Mott insulators share characteristics with supercooled liquids. Such distinctions have important implications on superconductivity. We discuss the evolution of dynamic atomic correlations in liquid with temperature, and a possible effect of dynamic correlations on the high-temperature superconductivity in the cuprates.

DOI
10.3390/condmat9010012

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Liquid and gas are distinct in their extent of dynamic atomic correlations; in gas atoms are almost uncorrelated whereas they are strongly correlated in liquid. This distinction applies also to electronic systems. Fermi liquids are actually gas-like, whereas strongly correlated electrons are liquid-like. Doped Mott insulators share characteristics with supercooled liquids. Such distinctions have important implications on superconductivity. We discuss the evolution of dynamic atomic correlations in liquid with temperature, and a possible effect of dynamic correlations on the high-temperature superconductivity in the cuprates.
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We summarize recent theoretical results of our group concerning the electronic states of the strongly correlated fermions at nonzero temperature. The state of almost localized fermions is discussed within a mean-field approach for auxiliary bosons, both in the narrow-band (Section 2) and in the hybridized band (Section 3) cases. This state represents a metallic state of correlated fermion systems (such as V{sub 2}O{sub 3}) below the Mott-Hubbard localization threshold. The Fermi liquid state does not describe properly the properties of narrow band electrons in the large Hubbard -- U limit beyond the localization threshold. Therefore, in Section 4 and 5 we introduce a phenomenological concept of statistical spin liquid which describes principal features of a crossover from a high-temperature superconductor to the Mott insulator for a two-dimensional system. It also reproduces the main features of the phase diagram for La{sub 2-x}Sr{sub x}CuO{sub 4} system, which is modelled by a planar structure.
In this brief overview, I address some of the fundamental topics related to the physics of strongly correlated fermions, which have been also the subject of my research. After addressing the question why the field has a fundamental meaning, we next turn to the specific problems with their simple theoretical description. Those topics are: (i) the concept of spindependent masses of heavy particles and its subsequent experimental verification; (ii) the correlated metal–insulator transitions of the Mott–Hubbardtype; (iii) real space pairing and its subsequent experimental verification for high-temperature superconducting cuprates. I mention also the persistence of quantum spin and charge excitations in the superconducting phase. All those phenomena confirm the view that the strongly correlated fermionic \nsystems represent a new class of quantum liquids, with some properties quantitatively different than those of the Landau Fermi liquids. Namely, they can be classified as those that fall in between those of the anomalous Landau Fermi liquid and localized-magnetic-moment system.
We investigate the effect of strong disorder on a system with strong electronic repulsion. In the absence of disorder, the system has a d-wave superconducting ground state with strong non-BCS features due to its proximity to a Mott insulator. We find that while strong correlations make superconductivity in this system immune to weak disorder, superconductivity is destroyed efficiently when disorder strength is comparable to the effective bandwidth. The suppression of charge motion in regions of strong potential fluctuation leads to the formation of Mott insulating patches, which anchor a larger nonsuperconducting region around them. The system thus breaks into islands of Mott insulating and superconducting regions, with Anderson insulating regions occurring along the boundary of these regions. Thus, electronic correlation and disorder, when both are strong, aid each other in destroying superconductivity, in contrast to their competition at weak disorder. Our results shed light on why zinc impurities are efficient in destroying superconductivity in cuprates, even though it is robust to weaker impurities.
It is very important to elucidate the mechanism of superconductivity for achieving room temperature superconductivity. In the first half of this paper, we give a brief review on mechanisms of superconductivity in many-electron systems. We believe that high-temperature superconductivity may occur in a system with interaction of large-energy scale. Empirically, this is true for superconductors that have been found so far. In the second half of this paper, we discuss cuprate high-temperature superconductors. We argue that superconductivity of high temperature cuprates is induced by the strong on-site Coulomb interaction, that is, the origin of high-temperature superconductivity is the strong electron correlation. We show the results on the ground state of electronic models for high temperature cuprates on the basis of the optimization variational Monte Carlo method. A high-temperature superconducting phase will exist in the strongly correlated region.
We use the concept of generalized (almost localized) Fermi Liquid composed of nonstandard quasiparticles with spin-dependence effective masses and the effective field induced by electron correlations.This Fermi liquid is obtained within the so-called statistically-consistent Gutzwiller approximation (SGA) proposed recently [cf.J. Je ¸drak et al., arXiv: 1008.0021] and describes electronic states of the correlated quantum liquid.Particular emphasis is put on real space pairing driven by the electronic correlations, the Fulde-Ferrell state of the heavy-fermion liquid, and the d-wave superconducting state of high temperature cuprate superconductors in the overdoped limit.The appropriate phase diagrams are discussed showing in particular the limits of stability of the Bardeen-Cooper-Schrieffer (BCS) type of state.