R.S. Markiewicz

Correlation of Tc with structure in the density of states in the new high-Tc superconductors

Abstract The variation of T c with hole concentration in the new copper oxide superconductors can readily be understood in terms of a peak in the density of states associated with the CuO 2 planes. The data are consistent with either simple phonon-mediated pairing or an indirect excitonic pairing. Effects due to interlayer coupling are considered. The sharp decrease of T c near half-filling is probable due to strong spin fluctuations.

Van Hove excitons and high-Tc superconductivity: (VI) Properties of the exitations

Abstract Two-dimensional van Hove singularities are associated with an unusual form of excitonic quasiparticle, which dominates many of their physical properties. Here, the polarizability of these excitons is calculated, and some of the roles they play in the new high- T c superconductors are discussed. In particular, a discussion of their contribution to the anomalous normal-state properties (optical conductivity) and to the tetragonal-orthorhombic and charge-density wave phase transitions is presented.

Van Hove excitons and high-Tc superconductivity VIIIA: Valence bond density waves

Abstract It has recently been shown that an important role of correlation effects is to renormalize the band structure to be more ‘Hubbard-like’ at half-filling, driving a Mott transition. Using this insight, the density wave (DW)-superconductivity competition in the high- T c oxides is reexamined. It is found that both the low-temperature orthorhombic (LTO) and the low-temperature tetragonal (LTT) transitions in La 2− x Ba x CuO 4 (LBCO) and related compounds are driven by the strong nesting of the van Hove singularity - the LTT as a static and the LTO a dynamic Jahn-Teller effect. A mean-field theory of the LTO phase is presented, in terms of a coherent superposition of charge DWs or a ‘valence bond density wave’. The resulting DW-superconductivity phase diagram strongly resembles that found in LBCO. Connections of the present model to the magnetic pseudogap and to one-dimensionality are discussed.

Van Hove excitons and high-Tc superconductivity VIIIB. vHs - Jahn-Teller effect

Abstract This paper considers the structurak phase transitions of La 2− x Ba x CuO 4 in a detailed model describing the tilting of the O octahedra (optical modes), strains (acoustic modes), and electrons near the two saddle points ( X, Y ) of the Brillouin zone. The model contains nonlinear terms in the tilting part, strain-tilting coupling, and electron-tilting coupling, which is new and important in discussing the various phases. The variables are divided into static and dynamic parts, and their equations of motion are linearized to give self-consistent solutions for the optical phonon frequencies. The above model and procedure are extension of previous works for structural phase transitions in A15 and Perovskite-type compounds. But a relation between the structural phase transitions and the van Hove singularity is newly discussed. The model is found to be a natural generalization to two dimensions of the Peierls transition of a one-dimensional metal. The resulting equations are used to fit the temperature (and wave number) dependence of the optical phonon frequencies as measured by neutron and Raman scattering. It is concluded that phonon softening associated with the low-temperature orthorhombic (LTO) transition can be described equally well either by a pure phonon model with anharmonicity or by an electron-phonon model reflecting the van Hove singularity. It is suggested that the latter model is relevant in describing the doping dependence of the structure as well as superconducting and magnetic transitions. The results suggest that the LTO phase may be a dynamic Jahn-Teller (JT) phase, involving tunneling among local quasi-static JT distortions, with the low-temperature tetragonal phase being a static JT phase.

Van Hove excitons and high-Tc superconductivity V: Electron-phonon interaction

Abstract A model is developed for electron-phonon interaction in the new superconducting oxides, showing that the system is nearly unstable with respect to a charge density wave, but that weak interlayer coupling generally prevents the establishment of true long-range order. It is shown that the associated mode softening produces a significant Tc enhancement, but probably not large enough to fully account for the experimental results. Suggestions are made for an additional coupling mechanism, probably associated with fluctuations into the ordered phase.

Van Hove excitons and high-Tc superconductivity VII: Gap equation with pair breaking

Abstract Detailed calculations are presented for the superconducting gap and critical temperature of a van Hove superconductor. The calculations are modified to account for a number of complicating factors, including interlayer coupling, strong coupling, and depairing effects due to real phonon scattering and spin scattering. The calculations are compared to experimental data on the isotope effect, spin-lattice relaxation time T 1 , and magnetic penetration depth, and satisfactory agreement is found. Power law corrections, particularly in T 1 , are suggestive of a gap zero.

Van Hove singularity and high-Tc superconductivity VI: Interlayer coupling

Abstract The role of interlayer coupling in smearing out the density of states peak associated with the van Hove singularity is explored. It is found that the logarithmic singularities persist under arbitrarily large intracell interlayer coupling. Furthermore, the effects of intercell coupling are generally much weaker than a naive estimate would suppose, and in many cases of interest, the logarithmic singularities persist in the presence of large intercell coupling as well. Finally, it is found that interlayer coupling does not reduce the transition temperature unless the interlayer hopping energy is greater than Tc.

Van Hove exciton-cageons and high-Tc superconductivity: VIIID. Solitons and nonlinear dynamics

Abstract The low-temperature orthorhombic (LTO) phase transition in La 2−χ Sr χ CuO 4 can be interpreted as a dynamic Jahn-Teller effect, in which the degenerate electronic states are associated with the large densities of states at the two van Hove singularities. The equations describing this phase are strongly nonlinear. This paper illustrates some consequences of the nonlinearity, by presenting a rich variety of exact nonlinear wave solutions for the model. Of particular interest are soliton lattice solutions: arrays of domain walls separating regions of local-low temperature tetragonal (LTT) symmetry. These arrays have a macroscopic average symmetry higher than LTT. These lattices can display either orthorhombic (“orthons”) or tetragonal (“tetrons”) symmetry, and can serve as models for a microscopic description of the dynamic JT LTO and high-temperature tetragonal phases, respectively.

The role of the Lifshitz point in high-Tc superconductivity

Abstract The importance of the two-dimensional van Hove singularity for high-temperature superconductivity is discussed. A modified Bilbro-McMillan hamiltonian is introduced, in which an “excitonic” pairing process arises naturally. the resulting gap equation has highly non-BCS solutions, with the possibility of 2Δ(0)>3.53k B T c .

Flux creep in high-Tc superconductors: melting or thermal depinning?

Abstract A number of different theories have been advanced to account for the low critical currents found experimentally in the various copper oxide superconductors, particularly the layered compounds based on Bi and Tl at temperatures above 40 K ( T ⪡ T c ). This paper reviews and critiques the various theoretical approaches. It is suggested that, whereas a thermally-activated flux flow theory can qualitatively describe the experimental observations, the rapid temperature variation of the effective pinning potential is probably due to a melting of the flux lattice.