Bound-electron pairs within a repulsive Hubbard model in two-coupled linear chains

The study of electronic correlation in multiple layer materials provides an opportunity to understand the different pairing mechanism, their importance can be traced to the discovery of high superconductors, superconductivity for a magic-angle in graphene lattices and others. In this work, we analyzed the two-interacting fermions in two-coupled periodic chains (ladder) within an attractive or repulsive potential, we obtain an analytical solution using the real-space mapping method. This real-space method is based on mapping the correlated many-body problem onto an equivalent tight-binding problem in a higher dimensional space. With this in mind, our ladder problem maps into a one-particle four dimensional lattice, which finally can be projected into an effective lattice of states in three dimensions. Two kind of solutions have been found, the antisymmetrical solution, which reduce the problem to two independent linear chains (one without impurities and the other with a central impurity) and the symmetrical solution corresponding to a ladder with an impurity. The latter solution is quite interesting since it allow us also to observe the new bound-electron pairs for E < 0 in a repulsive potential (U > 0).