Itinerant Vibrons and High-Temperature Superconductivity *
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ITINERANT VIBRONS AND HIGH-TEMPERATURE SUPERCONDUCTIVITY* John B. Goodenough Texas Materials Institute, ETC 9.102 University of Texas at Austin, Austin, TX 78712-1063 ABSTRACT The La2-xSrxCuO4 phase diagram is interpreted within the framework of a transition from localized to itinerant electronic behavior. In the underdoped region 0 < x < 0.1, holes in the x2 – y2 band are not small polarons; each occupies a mobile correlation bag of 5 to 6 copper centers at temperatures T > TF, a spinodal phase segregation into the parent antiferromagnetic phase and a polaron liquid is accomplished below TF by cooperative oxygen displacements. In the overdoped compositions x > 0.25, holes are excluded from strong-correlation fluctuations within a Fermi liquid. In the intermediate range 0.1 < x < 0.25, the polaron liquid formed below room temperature changes character with increasing x and decreasing T. In the polaron liquid, mobile two-hole bags of four copper centers order with decreasing temperature into alternate CuO-Cu rows of a superconductive CuO2 sheet at a critical composition xc ≈ 1/6. It is argued that hybridization of itinerant electrons with optical-mode phonons propagating along the Cu-O-Cu rows produces heavy electrons responsible for high-temperature superconductivity. *
Dedicated to J. M. Honig on his retirement in recognition of his long-time interest in the transition from localized to itinerant electronic behavior in solids.
INTRODUCTION Of all the copper-oxide superconductors, the oxygen-stoichiometric system La2-xSrxCuO4, 0 ≤ x ≤ 0.3, allows the most straightforward study of p-type high-temperature superconductivity in these materials. The number of holes in the CuO2 sheets is given unequivocally by x; and in the solid-solution range 0 ≤ x ≤ 0.3, the system changes with increasing x from an antiferromagnetic insulator to a superconductor and, finally, to a non-superconductive metal. Superconductivity appears below a critical temperature Tc in a phase having a narrow solidsolution range of intermediate composition 0.15 1) distortion of the CuO6/2 octahedra leaves the (3z2-r2) orbitals filled; the operative bands are the antibonding (x2-y2) bands. The lower (x2-y2) band, which corresponds to the Cu(III)/Cu(II) couple, is pinned to the top of the O2-:2p6 bands because the states are antibonding with respect to the Cu-O interactions; they retain the (x2-y2) character because the O-2pσ orbitals are strongly hybridized with the Cu-3d x2-y2 orbitals. The crystal-field x2-y2 orbitals may be written as ψ x2 - y2
=
Nσ(f x 2 - y 2 – λσφσ – λsφs)
(2)
where f x 2 - y 2 is the atomic 3d orbital, φσ and φs are the appropriately symmetrized O-2pσ and 2s orbitals of the four oxygen near neighbors in the CuO2 sheet, and the covalent-mixing parameters are λσ ≡ bpσ/∆Ep >> λs ≡ bsσ/∆Es, where ∆Ep and ∆Es are the energies required to transfer an electron from an O-2pσ or 2s orbital to the empty Cu(II)/Cu(I) couple; bpσ and bsσ are the electron-energy-transfer (resonance) integrals for these electron transfers. In La2CuO4, the
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