Momentum and energy dependences of the single-particle self-energy in two-dimensional Fermi liquids

In this thesis I investigate two dimensional Fermi liquid behavior for a parabolic band structure and a tight binding band structure. I discuss the normal state properties of high Tc cuprate superconductors as an application.; In the first part, the leading momentum, frequency and temperature dependences of the single-particle self-energy and the corresponding term in the entropy of Fermi liquid with the parabolic band structure is calculated in the repeated scattering case. The crossover from a low temperature behavior, T 2 ln T, to a high temperature behavior, T, in the imaginary part of the self-energy is discussed. The linear behavior in temperature of the imaginary part of the self energy has been understood as a non-Fermi liquid behavior. In the second part, I study the x2pInx p behavior of the imaginary part of the self-energy quantitatively in the second order calculation in the parabolic band structure in the low density limit. The contributions from the class of the particle-hole and the particle-particle diagrams are discussed in this limit and compared with these contributions in the 3D case.; The Hubbard model is considered in the studies of two dimensional Fermi liquid in the last part. The Fermi surface develops from a circle to a square as the band is filled. The single-particle Green's function is calculated in the particle-hole channel as a function of the chemical potential. The anisotropies in the density-density correlation function which are responsible for the anisotropy of the single-particle self-energy are studied. I show that the particle-particle channel does not contribute to the leading corrections to the Fermi liquid. The detailed calculation of the off-shell self-energy is investigated for different values of momentum. The spectral function which is expressed by the off-shell self-energy is investigated as a function of doping for two different directions in momentum space, (1, 0)p and (1, 1)p. I show that the width at half-maximum of the peak in the spectral function is approximated by the imaginary part of the on-shell self-energy. The absence of pseudogap behavior in the spectral function shows that a weak coupling treatment of the Hubbard model does not describe the normal state properties of the cuprates.