High-temperature superconductivity and charge segregation in a model with strong long-range electron–phonon and Coulomb interactions

An analytical method of studying strong long-range electron–phonon and Coulomb interactions in complex lattices is presented. The method is applied to a perovskite layer with anisotropic coupling of holes to the vibrations of apical atoms. Depending on the relative strength of the polaronic shift Ep and the inter-site Coulomb repulsion Vc, the system is either a polaronic Fermi liquid, Vc > 1.23Ep , a bipolaronic superconductor, 1.16Ep < Vc < 1.23Ep , or a charge segregated insulator, Vc < 1.16Ep . In the superconducting window, the carriers are mobile bipolarons with a remarkably low effective mass. The model describes the key features of the underdoped superconducting cuprates.  2002 Elsevier Science B.V. All rights reserved. PACS: 74.20.Mn; 71.38.-k; 71.38.Mx There is clear experimental [1–5] and theoretical [6–15] evidence for strong electron–phonon (el– ph) interaction in high-Tc superconducting cuprates (HTSC). Electron correlations are also important in shaping the Mott–Hubbard insulating state of parent undoped compounds [16]. The theory of high-Tc cuprates must treat both interactions on equal footing as was suggested some time ago [6]. In recent years many publications addressed the fundamental problem of competing el–ph and Coulomb interactions in the framework of the Holstein–Hubbard model * Corresponding author. E-mail address: [email protected] (P.E. Kornilovitch). [11–15] where both interactions are short-range (onsite). The mass of bipolaronic carriers in this model is very large and the critical temperature is suppressed down to a Kelvin scale. However, in the cuprates the screening is poor so that the el–ph interaction necessarily has to be long-range. Motivated by this fact, we have proposed that a long-range Fröhlich, rather than short-range Holstein, interaction should be the adequate model for the cuprates [17,18]. Differently from the usual continuum Fröhlich model (for review see [6,7]), we introduced a multipolaron Fröhlich-like lattice model with electrostatic forces fully taking into account the discreteness of the lattice, finite electron bandwidth, and the quantum nature of phonons. A single small polaron with the Fröhlich interaction was discussed long time ago [19]. Analytical [17] and ex0375-9601/02/$ – see front matter  2002 Elsevier Science B.V. All rights reserved. PII: S0375-9601(02)0 06 84 -9 A.S. Alexandrov, P.E. Kornilovitch / Physics Letters A 299 (2002) 650–655 651 act Monte-Carlo [18] studies of the simple chain and plane lattices with a long-range el–ph coupling revealed a several-order lower effective mass of this polaron than that of the small Holstein polaron. Later, the polaron and bipolaron cases of the chain model were analyzed in more detail in Refs. [20] and [21], confirming low masses of both types of carriers. Qualitatively, a long-range el–ph interaction results in a lighter mass because the extended lattice deformation changes gradually as the carrier moves through the lattice. In this Letter, we study a realistic multi-polaron model of the copper–oxygen perovskite layer which is the major structural unit of the HTSC compounds. The model includes the infinite on-site repulsion (Hubbard U term), long-range inter-hole Coulomb repulsion Vc, and long-range Fröhlich interaction between in-plane holes and apical oxygens. We find that, within a certain window of Vc, the holes form inter-site bipolarons with a remarkably low mass. The bipolarons repel and the whole system is a superconductor with a high critical temperature. At large Vc, the system is a polaronic Fermi liquid and at small Vc it is a charge segregated insulator. To deal with the model’s considerable complexity we first describe a theoretical approach that makes the analysis of complex lattices simple in the strong coupling limit. The model Hamiltonian explicitly includes long-range electron–phonon and Coulomb interactions as well as kinetic and deformation energies. An implicitly present infinite Hubbard term prohibits double occupancy and removes the need to distinguish fermionic spins. Introducing fermion operators cn and phonon operators dmα, the Hamiltonian is written as