Effects of finite pair binding energy in a model of a superconductor with local electron pairing

Abstract

Abstract A simple model of a superconductor with very short coherence length is studied for arbitrary electron density. The tight binding hamiltonian consists of the inter-site charge exchange term J , determining the hopping of electron pairs, and the effective on-site interaction U . The evolution of phase diagrams, superconducting critical temperature T c and critical fields are determined as functions of interaction parameters and electron density, and the temperature dependences of the electron pair concentration, magnetic susceptibility and specific heat are established. There are two well defined regimes of the model. In the local pair limit i.e. for large pair binding energies E b ( E b / k B T c ⪢1) the superconducting transition occurs through Bose condensation of preexisting pairs, whereas in the opposite case, i.e. for E b / k B T c ≲1, the transition is determined by pair breaking excitations and there are essentially no preformed pairs above T c . It turns out that a crossover between the two regimes, occurring with increasing U , is smooth.