Bond-Length Fluctuations in the Copper-Oxide Superconductors
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Bond-Length Fluctuations in the Copper-Oxide Superconductors John B. Goodenough Texas Materials Institute, University of Texas at Austin, Austin, TX 78712
ABSTRACT The phase diagram of La2-xSrxCuO4 is interpreted. From the virial theorem, it is argued that the cross-over from localized to itinerant electronic behavior in the range 0 < x < 0.3 is characterized by fluctuations between two equilibrium Cu-O bond lengths. Cooperative local fluctuations give rise to one-hole correlation bags of 5 to 6 copper centers on the underdoped side, to strong-correlation fluctuations in an itinerant-electron matrix on the overdoped side. Spinodal phase segregation between an antiferromagnetic, insulating parent phase and the superconductive phase occurs in the underdoped compositions, between the superconductive phase and the metallic overdoped phase on the other side of the phase diagram. Ordering of the fluctuations into a travelling bipolaronic charge-density/spin-density wave of composition x ≈ 1/6 yields heavy fermions of symmetry (x2 - y2) coexisting with light electrons; the high-temperature superconductive pairs are condensed out from the heavy fermions. INTRODUCTION It is widely accepted that bond-length fluctuations are associated with orbital fluctuations at Jahn-Teller ions in an oxide. Indeed, it was this recognition that led K. Müller to explore the copper oxides for high-temperature superconductivity. However, the copper-oxide superconductors all have intergrowth structures, and the degeneracy of the σ-bonding e orbitals at the Cu atoms in the superconductive CuO2 sheets is removed by the crystal symmetry. Therefore, orbital fluctuations are not anticipated except for those associated with a pseudo-JahnTeller deformation [1]. On the other hand, bond-length fluctuations can also occur at a crossover from localized to itinerant electronic behavior [2]; and in the mixed-valent copper-oxide superconductors, there is a crossover from localized-electron behavior in the parent compounds to itinerant-electron behavior in the overdoped compounds. Superconductivity appears to occur in a unique thermodynamic phase found in the narrow compositional range of the crossover, and there is mounting experimental evidence that bond-length fluctuations are a critical feature of the superconductive phase. This paper points out the origin of these fluctuations and illustrates their consequences with an interpretation of the phase diagram of the La2-xSrxCuO4 system. It is concluded that theoretical attempts to account for high-temperature superconductivity in the copper oxides cannot be based on spin-spin exchange interactions alone. THE VIRIAL THEOREM The theoretical argument for bond-length fluctuations at a crossover from localized to itinerant electronic behavior in perovskite-related oxides is most simply argued with the aid of the virial theorem, which states that for central force fields 2 + = 0
(1) E3.1.1
where is the mean kinetic energy of a system of particles and is their mean potential energy. The transition from localized
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