Thermodynamics of s ± -to- s + + transition in iron pnictides in the vicinity of the Born limit
To study the thermodynamic properties of the disorder-induced transition between �± and �++ superconducting gap functions, we calculate the grand thermodynamic potential Ω in the normal and the superconducting states. An expression for the difference between the two, ΔΩ, is derived for a two-band model for Fe-based systems with nonmagnetic impurities. The disorder is considered in a �-matrix approximation within the multiband Eliashberg theory. In the vicinity of the Born limit near the �±-to-�++ transition, we find two solutions obtained for opposite directions of the system's evolution with respect to the impurity scattering rate. By calculating the change in entropy ΔS and the change in the electronic specific heat ΔC from ΔΩ, we show that such a hysteresis is not due to the time-reversal symmetry breaking state, but that it instead points to the first order phase transition (PT) induced by the nonmagnetic disorder. Based on the ΔΩ calculations, a phase diagram is plotted representing the energetically favorable �± and �++ states and the transition between them. At finite temperature, a first order PT line there is limited by a critical end point. Above that point, the sharp �±→�++ transition transforms into a crossover between �± and �++ states.