Vortices in Hubbard Superconductors: A Bogoliubov-de Gennes Approach

Based on the Bogoliubov-de Gennes formalism, we study vortices with quantum magnetic fluxes in two-dimensional supercells, when an external magnetic field (B) is applied to s-, d-, and anisotropic s-wave superconductors. This study is carried out by using a generalized Hubbard model including negative U and V, as well as a nearest-neighbor correlated hopping interaction (Δt). The self-consistent calculation of the superconducting gap (Δ) shows the formation of vortices in real space, whose structure depends on the electron-electron interaction. Furthermore, the supercell averaged Δ as a function of B reveals qualitatively different behaviors for the three analyzed pairing interactions. Finally, the results suggest that the d-wave superconducting states have larger second critical magnetic fields than those corresponding to isotropic and anisotropic s-wave ones.