Superconductivities of high-T_c materials and alkali compounds of Buckminsterfullerene

Citation

Chen, Guanhua (1992) Superconductivities of high-T_c materials and alkali compounds of Buckminsterfullerene. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/chz3-cq25. https://resolver.caltech.edu/CaltechTHESIS:10132009-131816426

Abstract

This thesis is composed of two chapters. Chapter I is an investigation of the spin wave spectrum of the two-dimensional spin-1/2 Heisenberg model and its relevance to high-T_c superconducting materials. Chapter II is a study on another interesting family of superconductors, the alkali compounds of Buckyminsterfullerene A_xC_(60). The electron-phonon coupling constant of one member of these compounds, K_3C_(60), has been calculated and discussed in the context of the phonon-mediated superconducting mechanism. Chapter 1 consists of two projects. The first project is an exact diagonalization of a 4 x 4 S = 1/2 Heisenberg model. Energy vs. momentum spectra is derived and compared with the dynamic structure factors. The comparison shows that spin wave or magnon of a certain momentum corresponds to the lowest spin triplet state of that particular momentum. The second project, an extension of the first, is a Projector Monte Carlo simulation of 2D S = 1/2 Heisenberg square lattices of size 4 x 4, 6 x 6, 8 x 8 and 12 x 12. The lowest lying spin wave spectrum has been obtained for each of the above lattices, and the extrapolation to the infinitely large 2D square lattice has been derived. These results suggest that the exact spectrum for the infinite lattice is that of linear magnon with an overall renormalization factor. These results are also used to infer the value of the exchange energy from inelastic neutron scattering experiments of a high-T_c superconductor La_2CuO_4. The first part of Chapter 2 is a MNDO study of the electronic structure of a C_(60) molecule; this study excludes a proposed mechanism for the superconductivity in A_xC_(60), namely, Stability of Molecular Singlets ("SMS"). Secondly, Chapter II describes an investigation of the electron-phonon interaction caused by the changes of the electron-ion coulomb interactions, i.e., the static electron-phonon coupling. An accurate formalism based on the force field and phonon spectrum available is established to calculate the electron-phonon coupling matrix. This formalism includes exactly the available information about the phonon eigenvectors and eigenenergies and about the localized Wannier orbital for electrons in the conduction bands. The major contributions to the static electron-phonon coupling is found from the low frequency intermolecular phonon modes. Thirdly, a study on the electron-phonon coupling caused by the responses of the local electronic states to the vibrations of a C_(60) molecule (i.e., dynamic electron-phonon coupling) is presented. The study concludes that the dynamic coupling is strong enough to be relevant to the superconductivity in A_xC_(60). Finally, various properties related to the superconducting phase have been calculated, and are compared with the experimental results. On the basis of all these, an experiment is proposed to confirm our findings, and to determine the superconductivity mechanism in A_xC_(60) systems.

Thesis Files