Characteristics of Fermion Pairs with d- and extended s-wave Symmetries around BE-BCS Crossover

We study BE-BCS crossover features for electron pairs with $d_{x^2-y^2}$ and extended-s ($s^*$) symmetries on a quasi-2D square lattice. The pairing interaction is obtained from an extended Hubbard model with on-site repulsion U, and nearest-neighbor attraction V. We calculate various quantities for different filling f and V: Chemical potential $\mu$(V,f), gap $\Delta$(V,f), coherence length $\xi$(V,f). Tightly-bound BE pairs appear at some characteristic $V_b(f)$ at both small and large fillings for both symmetries. At the BE-BCS crossover, the quasiparticle distribution function $v_k^2$ for d-wave is strikingly different from that for $s^*$ wave: While for $s^*$ wave, the central peak in $v_k^2$ diminishes continuously, for $d_{x^2-y^2}$, it vanishes abruptly at the crossover, and redistributes around $(\pm \pi, 0), (0,\pm \pi)$ in the Brillouin zone. The Fourier transform, $v_r^2$ exhibits a ``checkerboard'' pattern. While the general features may be of relevance to the BE-BCS crossover in Fermi systems, the single-particle feature may be of relevance to the field of high $T_c$ cuprates near the pseudogap region. We also explore the density collective modes around the BE-BCS crossover using functional integral techniques within a 1-loop approximation.