Thermodynamics of $s_{\pm }-to-s_{++}$ transition in iron pnictides in the vicinity of the Born limit

Abstract

To study thermodynamical properties of the disorder-induced transition between $s_{\pm }$ and $s_{++}$ superconducting gap functions, we calculate the grand thermodynamic potential $\Omega$ in the normal and the superconducting states. Expression for the difference between the two, $\Delta \Omega$, is derived for a two-band model for Fe-based systems with nonmagnetic impurities. The disorder is considered in a $\mathcal{T}$-matrix approximation within the multiband Eliashberg theory. In the vicinity of the Born limit near the $s_{\pm }$-to-$s_{++}$ 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 $\Delta S$ and the change in electronic specific heat $\Delta C$ from $\Delta \Omega$, we show that such a hysteresis is not due to the time-reversal symmetry breaking state, but it rather points out to the first order phase transition induced by the nonmagnetic disorder. Based on the $\Delta \Omega$ calculations, phase diagram is plotted representing the energetically favourable $s_{\pm }$ and $s_{++}$ states and the transition between them. At finite temperature, a first order phase transition line there is limited by a critical end point. Above that point, the sharp $s_{\pm }\to s_{++}$ transition transforms to a crossover between $s_{\pm }$ and $s_{++}$ states.

9 pages, 7 figures This is the version of the article before peer review or editing, as submitted by an author to Superconductor Science and Technology journal. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at https://doi.org/10.1088/1361-6668/adc8dd