Reentrant superconductivity due to inter-band off-diagonal hopping in a two-band superconductivity model

We present a possible phase diagram for the superconductivity state in a two-band scenario that includes contributions from the inter-orbital off-diagonal hopping term. Our model accounts for intra-band attractive electron–electron interactions that leads to the formation of superconducting Cooper pairs in each component band and for an inter-band attractive electron–electron interaction responsible for a single superconductive transition temperature $$T_\textrm{c}$$ T c in the model. Using a mean field approximation, we obtained an analytical equation for the superconducting critical temperature that includes contributions from a hybridization term due to the mixing of the two electron bands. For a numerical solution of this equation, we considered a band structure that reproduced as much as possible the situation in the Ba $$_{1-x}$$ 1 - x K $$_x$$ x Fe $$_2$$ 2 As $$_2$$ 2 pnictide superconductor material. Our possible phase diagram $$T_\textrm{c}$$ T c vs. N is obtained assuming that Cooper pairs in both electron bands have either s-wave or $$s^\pm $$ s ± -wave symmetry. The main result of our calculation is the existence of a complex phase diagram that at different inter-orbital hopping strengths can have one or two local maxima for the transition critical temperature $$T_\textrm{c}$$ T c . The electron concentration at which these maxima occur in the phase diagram can be tuned using the inter-orbital off-diagonal hopping term. Graphic abstract