Universality of superconducting gaps in overdoped Ba${}_{0.3}$K${}_{0.7}$Fe${}_2$As${}_2$ observed by angle-resolved photoemission spectroscopy

We have performed angle-resolved photoemission spectroscopy on the overdoped Ba${}_{0.3}$K${}_{0.7}$Fe${}_2$As${}_2$ superconductor ($T_c=22$ K). We demonstrate that the superconducting (SC) gap on each Fermi surface (FS) is nearly isotropic whereas the gap value varies from 4.4 to 7.9 meV on different FSs. By comparing with under- and optimally doped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$, we find that the gap value on each FS nearly scales with $T_c$ over a wide doping range ($0.25⩽x⩽0.7$). Although the FS volume and the SC gap magnitude are strongly doping dependent, the multiple nodeless gaps can be commonly fitted by a single gap function assuming pairing up to the second nearest neighbor, suggesting the universality of the short-range pairing states with the $s_{\pm }$-wave symmetry.

Figure 1

(a) Plot of ARPES intensity at $E_{\mathrm{F}}$ as a function of the in-plane wave vector measured at 10 K for the K0.7 sample (OD; $T_c=22$ K). The intensity is obtained by integrating the spectral intensity within $\pm 10$ meV with respect to $E_{\mathrm{F}}$. Solid curves show the schematic FSs. (b) ARPES intensity plot along the $\Gamma$-$M$ line as a function of binding energy and wave vector. Solid curves are guides for the eyes to trace the band dispersion. (c)–(h) ARPES intensity plots in the vicinity of $E_{\mathrm{F}}$ and (i)–(n) corresponding EDCs measured in the normal state (30 K) along cuts 1–6 indicated by green lines in (a). Dashed curves and dots are guides for the eyes. White vertical dashed lines in (c)–(h) represent the $\Gamma$-$M$ line. (o) Symmetrized EDCs of the blue (dark gray) curves in (i), (k), and (n).

Figure 2

(a) ARPES intensity plot as a function of binding energy and wave vector measured at 8 K near the $\Gamma$ point and (b) corresponding EDCs. Dashed curves and dots are guides for the eyes to trace the dispersion of the $\alpha$ and $\beta$ bands. EDCs at $k_{\mathrm{F}}$ points are indicated by blue (dark gray) curves in (b). (c) High-resolution EDCs near $E_{\mathrm{F}}$ at $T=8$ K and 30 K measured at a $k_{\mathrm{F}}$ point of the $\alpha$ band. (d) Schematic FSs of the K0.7 sample. (e)–(g) Symmetrized EDCs at 8 K measured at various $k_{\mathrm{F}}$ points of the $\alpha$, $\beta$, and $\gamma$ FSs indicated by filled circles in (d). The color of the spectra is the same as that of the circles. (h) Symmetrized EDCs at 30 K for representative $k_{\mathrm{F}}$ points on each FS.

Figure 3

(a) Schematic FSs and definition of the FS angle ($\theta$). (b) and (c) Polar plots of the SC gap size at 8 K for the (b) $\alpha$, $\beta$ and (c) $\gamma$ FSs as a function of $\theta$. Dashed circles show the averaged SC gap values on each FS. (d) Plot of the SC gap size as a function of $|$$\text{cos}{k}_x\hspace{0.5em}\text{cos}{k}_y$$|$. The dashed line and purple dots represent the best fit assuming the gap function $\left|\Delta \right|={\Delta }_0\left|\cos k_x\cos k_y\right|$ and $\left|\Delta \right|=|{\Delta }_1\hspace{0.5em}\text{cos}{k}_x\hspace{0.5em}\text{cos}{k}_y+{\Delta }_2(\text{cos}{k}_x+\text{cos}{k}_y)/2|$, respectively.

Figure 4

(a) and (b) Representative symmetrized EDCs in the SC state measured at $k_{\mathrm{F}}$ points of the (a) $\alpha$ and (b) $\beta$ FSs for the K0.7 (OD; $T_c=22$ K), K0.4 (OPD; $T_c=37$ K), and K0.25 (UD; $T_c=26$ K) samples. (c) Doping dependence of the averaged SC gap size on each FS. Colored curves show the SC gap size obtained by assuming constant $2\left|\Delta \right|/k_B{T}_c$ values (integers from 3 to 9). (d)–(f) Experimentally determined $k_{\mathrm{F}}$ points of the $\alpha$, $\beta$, and $\gamma /\delta$ bands [red (gray), blue (dark gray), and green (light gray) circles, respectively]. The $k_{\mathrm{F}}$ points of the $\gamma /\delta$ FSs are shifted by $Q=(-\pi ,0)$.