A Lanczos study of superconducting correlations on a honeycomb lattice

Abstract

In this thesis superconducting correlations on both a one-dimensional chain and a two-dimensional honeycomb lattice are analyzed using the t-J model Hamiltonian. Both systems use periodic boundary conditions and different electron fillings, and both are solved numerically using the Lanczos algorithm. In order to search for superconducting correlations in the ground state the pair-pair correlation and susceptibility functions are defined. In one dimension the correlation function, at lower electronic fillings, displayed appreciable, non-zero values for all pair-pair separations. In general, the one-dimensional results were consistent with the literature. However, the honeycomb results did not show such strong superconducting correlations, as the correlation function remained close to zero for most separation distances.