We derive an effective single-band Hubbard-type Hamiltonian for ${\mathrm{CuO}}_2$ planes in the cuprate high-${\mathit{T}}_{\mathit{c}}$ superconductors. The Hamiltonian includes both electron-electron repulsion and electron-phonon coupling to oxygen vibrational modes. The effective Hamiltonian is derived by mapping from the multiband constrained-density-functional-theory Hamiltonian to a one-band model. A Hartree-Fock mapping leads to t=0.66 eV, t’=-0.14 eV, and U=4.0 eV. Very similar parameters are obtained by exact diagonalization of finite clusters. The electron-phonon coupling to oxygen breathing modes gives λ=0.57 for s-wave and λ=0.35 for ${\mathit{d}}_{\mathit{x}}^2$-${\mathit{y}}^2$ pairing. d-wave superconductivity is predicted to occur at 30 K for doped ${\mathrm{La}}_2$${\mathrm{CuO}}_4$, while the strong Coulomb repulsion suppresses the s-wave ${\mathit{T}}_{\mathit{c}}$ to 10 K.

In order to investigate effects of the Coulomb correlation on the electron-phonon interaction in a strongly correlated system, the electron-phonon coupling constant (${\lambda }_{\mathrm{ph}}$) and the electron-spin-fluctuation coupling constant (${\lambda }_{\mathrm{sf}}$) are evaluated for the Hubbard Hamiltonian system. It is found that the Coulomb correlation in the Hubbard model gives rise to a phonon hardening and an enhancement of ${\lambda }_{\mathrm{ph}}$. Further, both ${\lambda }_{\mathrm{ph}}$ and ${\lambda }_{\mathrm{sf}}$ are found to be reduced significantly in overall magnitudes, if an effect of the finite bandwidth is taken into account. In particular, we have found that ${\lambda }_{\mathrm{ph}}$ becomes larger than ${\lambda }_{\mathrm{sf}}$ for a system with a nearly filled band, which indicates that a phonon-mediated BCS superconductivity may be possible in strongly correlated systems.

A theory of the t-J model in the presence of an external electromagnetic field is presented. The 1/N expansion for this model in the slave-fermion representation is developed, and it is shown that all the general properties of the theory are satisfied in every order of the 1/N expansion separately. A convenient procedure of the gauge fixing is suggested. It is shown that superconductivity may exist in this model even in the absence of the electron pairing. It is argued that experimental predictions of the theory might agree with the observed properties of the copper oxides.

We have developed a theory of transport phenomena for superconductors above ${\mathit{T}}_{\mathit{c}}$ in the fluctuating region in dirty and clean limits. We show that it is possible to construct a phenomenological theory based on Ginzburg-Landau equation and its gauge invariance, and as a result we can express the fluctuating corrections to the conductivity tensor in a magnetic field in terms of the classical conductivity and coherence lengths. We find that the sign of the Hall conductivity is universal and is determined by ∂ ln${\mathit{T}}_{\mathit{c}}$/∂ lnμ.

We present an ab initio pseudopotential local-density-functional calulation for the stoichiometric high-${\mathit{T}}_{\mathit{c}}$ cuprate ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$ using the plane-wave basis set. We have overcome well-known difficulties in applying pseudopotential methods to first-row elements, transition metals, and rare-earth materials by carefully generating norm-conserving pseudopotentials with excellent transferability and employing an extremely efficient iterative diagonalization scheme optimized for our purpose. The self-consistent band structures, the total and site-projected densities of states, the partial charges and their symmetry-decompositions, and some characteristic charge densities near ${\mathit{E}}_{\mathit{F}}$ are presented. We compare our results with various existing full-potential linear augmented-plane-wave and full-potential linear muffin-tin orbital calculations and establish that the ab initio pseudopotential method is competitive with other methods in studying the electronic structure of such complicated materials as high-${\mathit{T}}_{\mathit{c}}$ cuprates.

The magnetic and superconducting properties of the ${\mathrm{TISr}}_2$${\mathrm{Ca}}_{1\mathrm{-}\mathit{x}}$${\mathit{R}}_{\mathit{x}}$${\mathrm{Cu}}_2$${\mathrm{O}}_7$ [R=Pr (x=0.2–1.0); Tb (x=0.6 and 1.0)] system are reported. The observation of superconductivity in ${\mathrm{TISr}}_2$${\mathrm{Ca}}_{0.4}$${\mathrm{Pr}}_{0.6}$${\mathrm{Cu}}_2$${\mathrm{O}}_7$ (${\mathit{T}}_{\mathit{c}}$=74 K) suggests that the Pr ions are in the trivalent state. The value of the effective magnetic moment, ${\mathrm{\mu }}_{\mathrm{eff}}$=3.15${\mathrm{\mu }}_{\mathit{B}}$, for the ${\mathrm{TISr}}_2$${\mathrm{Ca}}_{0.4}$${\mathrm{Pr}}_{0.6}$${\mathrm{Cu}}_2$${\mathrm{O}}_7$ compound, lies between the free-ion values expected for ${\mathrm{Pr}}^{3+}$ (3.58 ${\mathrm{\mu }}_{\mathit{B}}$) and ${\mathrm{Pr}}^{4+}$ (2.54${\mathrm{\mu }}_{\mathit{B}}$). The reduced value of ${\mathrm{\mu }}_{\mathrm{eff}}$ for the ${\mathrm{Pr}}^{3+}$ ion is explained in terms of crystal-field effects. For ${\mathrm{TISr}}_2$${\mathrm{TbCu}}_2$${\mathrm{O}}_7$, the Tb magnetic moments order antiferromagnetically at 7.0 K, which is the highest magnetic ordering temperature among the known Tb-containing high-${\mathit{T}}_{\mathit{c}}$ related compounds. Superconductivity (${\mathit{T}}_{\mathit{c}}$=74 and 62 K) and antiferromagnetic ordering (${\mathit{T}}_{\mathit{N}}$=5 and 6.2 K) coexist in ${\mathrm{TISr}}_2$${\mathrm{Ca}}_{0.4}$${\mathit{R}}_{0.6}$${\mathrm{Cu}}_2$${\mathrm{O}}_7$ with R=Pr and Tb, respectively.

Shear-torque experiments have been performed on (NaCN${)}_{1\mathrm{-}\mathit{x}}$(KCN${)}_{\mathit{x}}$ mixed crystals, x=0.85, 0.45. The shear strain relaxation time follows an Arrhenius law. The results support recent molecular-dynamics simulations.

The highest coordination known in ionic ${\mathit{AX}}_2$ compounds is found in the orthorhombic cotunnite (${\mathrm{PbCl}}_2$) structure, in which the metal ion is in ninefold coordination. Four cotunnite-structured compounds, ${\mathrm{PbCl}}_2$, ${\mathrm{BaCl}}_2$, ${\mathrm{BaBr}}_2$, and ${\mathrm{SnCl}}_2$, were investigated under high pressure by x-ray diffraction and were found to undergo phase transitions to the same postcotunnite phase at pressures between 7 and 16 GPa. The high-pressure phase is monoclinic, of space group P${112}_1$/a, Z=8, with a structure in which the metal coordination number is ten, a value which up to the present has only been observed for covalent and metallic ${\mathit{AB}}_2$ compounds. This postcotunnite structure observed here is of considerable importance for the crystal chemistry of the ${\mathit{AX}}_2$ compounds as under ambient conditions over 400 compounds are isostructural to ${\mathrm{PbCl}}_2$ and many others transform to a cotunnite structure at high pressures, which up to the present was the final known step in the phase-transition sequence of these materials. This new phase is 4.5±0.5% denser than the cotunnite type in the csae of ${\mathrm{PbCl}}_2$ at 16 GPa.

Character tables and stereographic projections for five pentagonal and seven decagonal point groups have been given. According to our character formulas for quasicrystal tensors, the elastic constants up to cubic order have been deduced. By generalized elasticity theory, linear elastic energies, Hooke’s laws, and equilibrium equations have also been obtained. The results show, like trigonal and hexagonal point groups, both five pentagonal and seven decagonal point groups can be divided into two Laue classes. They are 5, 5¯ and 5m, 52, 5¯m; 10, 10¯, 10/m and 10mm, 10 2 2, 10¯m2, 10/mmm, respectively, and all the point groups belonging to the same Laue class possess the same elastic properties.

The electronic energy spectrum and localization of the wave functions for a class of one-dimensional generalized Fibonacci quasilattices, whose substitution rules are A→ABB and B→A, have been studied. It has been found that the spectrum has a peculiar trifurcating structure and there are three kinds of wave functions in the spectrum: extended, localized, and intermediate states. The middle part of the central subband in every hierarchy of the spectra is always continuous and the corresponding wave functions are all extended while the rest of the wave functions are intermediate or localized, i.e., there exist mobility edges in the subband. For the whole spectra the mobility edges possess a type of hierarchical structure.

An ultra-small-angle x-ray-scattering study showed several orders of Bragg diffraction for an aqueous colloidal silica dispersion in a vertically held glass capillary, the first peak being at 150’’. The same profile was observed when the capillary was rotated around its axis by (60×m)° (where m is an integer). A different profile was found at (30+60×m)° with the first peak at 85’’. This showed that a bcc lattice was maintained with the (110) plane parallel to the capillary wall and with a lattice constant =3000 Å, ${\mathit{d}}_{110}$=2100 Å, and ${\mathit{d}}_{020}$=1500 Å. The closest interparticle distance (2${\mathit{D}}_{\exp }$) was 2600 Å while the average distance from the overall concentration (2${\mathit{D}}_0$) was 2900 Å, indicating the non-space-filling nature of the crystal.

We propose a scheme to study exactly the kinetic Ising model on fractals under the linear approximation. This enables us to obtain the critical slowing-down behavior of the longest relaxation time of the kinetic Ising model on a fractal exactly. As a result, we show that there are only two time scales in the relaxation process of the kinetic Ising model on a fractal cluster under the linear approximation; the critical dynamic exponent is always a constant that is unrelated to the temperature of the system and is equal to 2. The implication of our results to the linear approximation of the critical dynamics of the kinetic Ising model on fractals as well as to the time-dependent renormalization-group method is discussed.

We point out that in the large cell-to-cell renormalization-group transformations to obtain the thermodynamic free energy and order parameter of a phase-transition system, we need only iterate the transformations until the correlation length of the system is smaller than the linear dimensions of the cells. We apply this idea to obtain a very accurate order parameter for the site-random percolation model, which may be used to represent dilute magnets at low temperatures.

A room-temperature giant magnetoimpedance (GMI) effect has been observed in thin amorphous ribbons of the soft ferromagnetic alloy ${\mathrm{Co}}_{75\mathrm{-}\mathit{x}}$${\mathrm{Fe}}_{\mathit{x}}$${\mathrm{Si}}_{15}$${\mathrm{B}}_{10}$ at low fields, H<10 Oe. The size- and field-dependence of the effect are very sensitive to the annealing conditions and concentration x. The peak value of the magneto-impedance ratio is strongly dependent on the frequency of the measuring ac current. Values as large as 130% have been measured at 1 MHz in a sample with the zero-magnetostriction composition (x=4.6) properly annealed in a transverse field. We suggest that the frequency dependence of the GMI arises from electron scattering by ac current-induced domain-wall oscillations.

The temperature dependence of the interface magnetization at low temperature was investigated for Co/Cu superlattices by measuring the ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ NMR spectra. ${}_{}{}^{59}{}_{}{}^{}\mathrm{Co}$ NMR measurements in zero field indicate that the temperature dependence of the interface Co hyperfine field is larger than that of the inner bulk Co hyperfine field.

We consider a bilayer, consisting of two isotropic Heisenberg ferromagnetic monolayers coupled by a short-range effective exchange interaction perpendicular to the planes. We also add the dipolar interactions. We obtain the transverse one-spin, double-time Zubarev-Tyablikov Green’s functions in the random-phase approximation and therefrom we calculate the critical temperature ${\mathit{T}}_{\mathit{c}}$ and the zero-point spin deviation as functions of the dipolar anisotropy parameter defined as ${\mathit{E}}_{\mathit{d}}$=(g${\mathrm{\mu }}_{\mathit{B}}$${)}^2$S/${\mathit{a}}^3$${\mathit{J}}_{\mathrm{\parallel }}$, where a is the lattice constant of the magnetic square lattices and ${\mathit{J}}_{\mathrm{\parallel }}$ is the in-plane exchange constant. We show that ${\mathit{T}}_{\mathit{c}}$ decreases logarithmically to 0 as ${\mathit{E}}_{\mathit{d}}$ tends to 0. For finite ${\mathit{E}}_{\mathit{d}}$ the acoustic (lower) magnon branch has a linear dispersion relation (anisotropic) for small ${\mathbf{k}}_{\mathrm{\parallel }}$ when the interplanar coupling is finite, but it changes to the square root of ‖${\mathbf{k}}_{\mathrm{\parallel }}$‖ as both planes become uncoupled. In the case of simple cubic (001) kind of stacking of the two planes, we show that for small ‖${\mathbf{k}}_{\mathrm{\parallel }}$‖, the acoustic branch energy becomes imaginary as ${\mathit{E}}_{\mathit{d}}$ attains a critical value. Below this value, the bilayer exhibits long-range ferromagnetic order, as in a monolayer with dipolar and exchange interactions, with the layers aligned parallel. For ${\mathit{E}}_{\mathit{d}}$ larger than the critical value, this alignment is unstable.

Magnetic properties of layered antiferromagnets have been studied using correlated effective field (CEF) theory developed by M. E. Lines. This theory goes beyond mean-field theory and correctly reproduces the experimental results. The theory is used here to interpret the magnetic order parameter and the susceptibilities of the ${\mathrm{FePS}}_3$ compound, which is a layered antiferromagnet with a marked Ising anisotropy.

We have calculated exactly the critical temperature, within the conventional Eliashberg framework, for realistic couplings. Our more precise analytic calculation leads naturally to a ${\mathit{T}}_{\mathit{c}}$ higher than that given by McMillan’s formula, which is generally used. We give an accurate formula for ${\mathit{T}}_{\mathit{c}}$ in the coupling region λ≤1.

Existence of a large anisotropy of the superconducting energy gap in ${\mathrm{Bi}}_2$${\mathrm{Sr}}_2$${\mathrm{CaCu}}_2$${\mathrm{O}}_8$ was confirmed by angle-resolved photoemission. The gap size, Δ (the full superconducting energy gap being 2Δ), is 0–4 meV for the ΓX and ΓY directions while that of the ΓM¯ direction, 45° away from the former two, is 17–19 meV. Comparison with previous reports was made with regard to the symmetry of the superconducting order parameter. It was also found that the electronic structure of the normal state in the ΓY direction is considerably modified by the incommensurate superstructure in the BiO plane. In contrast, the size of superconducting gap is identical within the present accuracy for both ΓX and ΓY directions, suggesting that the superstructure has a negligible effect on the size of the superconducting energy gap.

Transport experiments show that the effective carriers in the cuprates scale with dopants. But it was found in recent photoemission experiments that doping builds electronic states into the undoped energy gap and that the Fermi surfaces are consistent with the local-density-approximation theory so that the effective carriers scale with the total carriers. These contradictory phenomena and some others in the cuprates can be understood in the frame of a consistent and nesting-independent incommensurate Hartree-Fock theory of the doped Hubbard model.