In addition to exploring the evolution of the gap or order parameter with density and interaction strength several quantities of broader interest, namely condensation energy, pair and phase coherence length, residual bosonic interaction, and specific heat jump at the critical temperature are calculated.
Next, to investigate pairing features on a 2D lattice, the extended Hubbard model with nearest neighbor (nn)and next-nearest-neighbor (nnn) hopping, on-site repulsive interaction and nearest-neighbor attractive interaction is employed. The evolution of the gap function and the chemical potential with density/filling for different pairing symmetries (extended s-wave and d-wave) for different values of interaction strength are studied. Significant differences between the particle distribution function of superfluid density between s-wave and d-wave pairing cases are obtained and discussed. These differences may have important consequences for unconventional superconductors and have broader range of validity than the specific model under consideration. We use topological methods to explore the topological aspects of the paired state and possible existence of non-trivial topological properties. The study appears to be promising for an understanding of the so-called ``pseudogap'' feature of high-Tc superconductors.
The research goes beyond mean-field approximation in studying collective modes of the BCS and BE pairing states. The most suitable way is the functional integral method that gives the Gaussian fluctuation matrix theory. Using this, the evolution of the speed of sound is deduced.