Theory of the quasi-one-dimensional electron gas coupled to phonons.

摘要

This thesis is a theoretical study of quantum one- and quasi-one-dimensional (1D) electron-phonon systems containing both electron-electron and electron-phonon interactions. We first consider a 1D Luttinger liquid coupled to a dispersion-less optical phonon mode. We obtain exact results for the optical conductivity and finite-temperature single-particle spectral function for the case in which the electron-electron and electron-phonon couplings are purely forward scattering. The spectral function calculation is extended to include backward scattering with a renormalization group treatment. The electronic dispersion contains a change in velocity at the phonon energy. If the backward scattering part of the electron-phonon interaction is not too strong compared to the forward scattering part, coupling to phonons also produces a pronounced peak in the spectral function at low energies. The spectral function is similar to angle-resolved photoemission data in the high-temperature superconductors; we take the quality of the comparison as evidence of the non-Fermi-liquid character of the measured spectra. Using a renormalization group method, we also study the zero-temperature phases of the interacting one-dimensional electron gas coupled to phonons. We study the dependence of the ground state on the electron-phonon and electron-electron coupling strengths, the screening length, electron bandwidth, phonon frequency, doping, and type of phonon. Analytic expressions are obtained for the weak-coupling quantum phase boundaries of the 1D extended Holstein-Hubbard model and the 1D extended Peierls-Hubbard model for general band-filling and phonon frequency. We discover cases in which a repulsive electron-electron interaction enhances superconductivity in the presence of a retarded electron-phonon interaction. The spin gap and low-temperature superconducting susceptibility are found to be strongly dependent on the deviation from half-filling (doping). For a quasi-1D array of weakly coupled, fluctuating 1D chains, we discover cases in which the superconducting transition temperature Tc exhibits a maximum as a function of doping. The effect of changing the ion mass (isotope effect) on Tc is found to be largest near half-filling and to decrease rapidly with doping. The isotope effect exponent for the spin gap is typically the opposite sign as the isotope effect exponent for Tc.