Superconducting specific heat jump $\Delta C_{\mathrm{el}}\propto T_c^{\beta }(\beta \approx 2)$ for K${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$

Abstract

We present a systematic study of the electronic specific heat jump ($\Delta C_{\mathrm{el}}$) at the superconducting transition temperature $T_c$ of K${}_{1-x}$Na${}_x$Fe${}_2$As${}_2$. Both $T_c$ and $\Delta C_{\mathrm{el}}$ monotonously decrease with increasing $x$. The specific heat jump scales approximately with a power-law, $\Delta C_{\mathrm{el}}\propto T_c^{\beta }$, with $\beta \approx 2$ determined by the impurity scattering rate, in contrast to most iron-pnictide superconductors, where the remarkable Bud'ko-Ni-Canfield (BNC) scaling $\Delta C_{\mathrm{el}}\propto T^3$ has been found. Both the $T$ dependence of $C_{\mathrm{el}}(T)$ in the superconducting state and the nearly quadratic scaling of $\Delta C_{\mathrm{el}}$ at $T_c$ are well described by the Eliashberg-theory for a two-band $d$-wave superconductor with weak pair-breaking due to nonmagnetic impurities. The disorder induced by the Na substitution significantly suppresses the small gaps leading to gapless states in the slightly disordered superconductor, which results in a large observed residual Sommerfeld coefficient in the superconducting state for $x>0$.

5 pages, 3 figures, and supplement

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