Bond asymmetry and high-Tc superconductivity

Journal ArticleWe propose a simple mechanism, anchored in weak-coupling BCS theory, which ties together the following facts: high Tc; quasi two dimensionality; orthorhombic distortion and/or disordered lines of oxygen; proximity to a metal-insulator transition; and anomalously small isotope effects

Ground state of interacting spins

Journal ArticleThe question is posed of how the ground state of the Heisenberg Hamiltonian H= - ΣFij Si-Sj depends on the magnitude s of N interacting spins, particularly in the case of long-ranged oscillatory interactions Fij. It is discussed whether fixing the geometry and the bond strengths Fij suffices to determine the nature of the spin correlations in the ground state, and a review is given of known instances when this is the case; those are special situations in ferromagnetism and antiferromagnetism when qualitative ground-state properties such as "lack of nodes" can be proved to be independent of s

Few-body problem on a lattice

Journal ArticleThe author explores some of the inherent simplifications of "quantum lattice physics." He distinguishes between fermions and bosons and analyzes the n-body problem for each, with n = 1,2,3... typically a small number. With delta-function (zero-range) interactions, the three-body problem on a lattice is manageable, and some results can even be extrapolated to n >_ 4. Such calculations are not limited to one dimension (where the well-known Bethe ansatz solves a number of n-body problems). On the contrary, studies cited are mainly in three dimensions and actually simplify with increasing dimensionality. For example, it is found that bound states of n >_ 3 particles in d >_ 3 dimensions are formed discontinuously as the strength of two-body attractive forces is increased, and are therefore always in the easily analyzed "strong coupling limit." In the Appendix, an exactly solved example from the theory of itinerant-electron magnetism illustrates how a rigorous solution to the few-body problem is capable of yielding information concerning the N-body problem

Phonon model of vacancy-interstitial pair formation in solids

Journal ArticleBonds between neighboring atoms in a solid are imperfect harmonic oscillators. Through consideration of the nonlinearities, it is shown that vacancy-interstitial defect pairs can be described in terms of phonon dynamical variables. The effective spring constants are determined by self-consistency requirements. An inhomogeneous solution is found to the equations of the self-consistent spring constants; it describes an atom breaking its bonds to its neighbors, resulting in a defect pair

Anomaly in spin-wave spectrum of magnetic metals

Journal ArticleIt is pointed out that in the band theory of magnetism the magnons have frequencies comparable to the Fermi energy. Therefore, in the calculation of the magnon spectrum of iron, nickel, cobalt, etc., it is the time- or frequency-dependent response function of the electrons which is used, and this function-in contrast with the static response function-does not have a "Kohn kink" at q=2ĸғ

Steady-state distribution function in dilute electron gases

Journal ArticleIt is usually assumed that optically created carriers in a photoconductor rapidly thermalize to a Boltzmann distribution, regardless of the generation and recombination mechanisms. However, it can be shown that this distribution which is characteristic of thermodynamic equilibrium is incompatible with the requirements of steady state. A variational principle is introduced to find the steady-state distribution, which is found to approach the Maxwell-Boltzmann function in the limit of strong thermal scattering. Interband scattering is found to be potentially a strong thermalizing influence, in addition to the intraband scattering usually considered. For a simple model semiconductor, significant deviations from the Boltzmann distribution are found to be possible at temperatures below a few degrees Kelvin. This result is then discussed in connection with certain experiments on germanium

Electron-phonon interaction in two dimensions: the case for strong coupling in high-Tc superconductors

Journal ArticleA particular model interaction between electrons and acoustic phonons is found to cause electrons to become weakly "self-trapped" for an arbitrary filling factor in d=2, but not in d=1 nor, for different reasons, in d>3. To the extent that electron kinetic energy is reduced in d=2, the electronic interactions become proportionally more effective. Among phonon-mediated interactions we identify a static anisotropic interaction, compatible with observed ordering of oxygen vacancies along privileged axes in YBa2Cu307-x, while other mechanisms encourage electron pairing and superconductivity

Long-ranged magnetic polarization effects

Journal ArticleTwo years ago a group1 at Bell Telephone Laboratories discovered an exceedingly long-ranged magnetic interaction among rare earth (RE) atoms dissolved in palladium. It is the purpose of the present note to suggest a theory for this phenomenon, which, it will be recalled, could not be explained by the Ruder man-Kittel interaction nor even by the longer ranged Yosida modification, without assuming an unreasonably small value of kғ

Accuracy of bosonization for localized interactions

Journal ArticleBosonization is commonly used to calculate the ground-state energy and the dynamics of simple model nonmagnetic impurities in metals. We analyze the accuracy of this procedure in the calculation of the ground-state energy of a simple, solvable, model

Exactly solvable model of a magnetic impurity

Journal ArticleA slight modification of the "mixing" term in Anderson's model of a magnetic impurity produces an exactly solvable model. Results of some preliminary calculations are given, and upper and lower bounds on Anderson's model are obtained by means of the exact solutions.