Pair-breaking effects induced by 3-MeV proton irradiation in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$

Pair-breaking effects induced by 3-MeV proton irradiations are examined in underdoped, optimally doped, and overdoped Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ single crystals in terms of suppression of the superconducting critical temperature $T_c$. The small residual resistivity (RR) in as-grown crystals shows the presence of negligible intrinsic scatterings, which makes this material a model system for studying the effect of artificially introduced scatterings. The RR and $T_c$ change linearly with the proton dose. As in the case of proton irradiation in Co-doped BaFe${}_2$As${}_2$, we do not detect any low-temperature upturns in resistivity attributable to magnetic scattering or localization. Regardless of K doping levels, the critical value of the normalized scattering rate is much higher than that expected in $s_{\pm }$-wave superconductors.

Figure 1

Temperature dependence of the resistivity in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ ($x=0.23$, 0.42, and 0.69). Inset: The resistivity as a function of $T^2$.

Figure 2

Temperature dependence of the resistivity in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ ($x=0.23$, 0.42, and 0.69) with doses of 0, 0.52, 1.0, 1.6, 2.1, 3.1, 4.8, 6.8, and 9.2$\times {10}^{16}$ ions/cm${}^2$. Broken lines represent fitting lines of $\rho ={\rho }_0+A{T}^2$.

Figure 3

Dose dependence of (a) $\Delta {\rho }_0\equiv {\rho }_0^i-{\rho }_0^0$ and (b) $T_c$ in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ ($x=0.23$, 0.42, and 0.69).

Figure 4

$T_c$ as a function of $\Delta {\rho }_0$ in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ ($x=0.23$, 0.42, and 0.69). Inset: The vertical axis is changed to $T_c/T_{c0}$.

Figure 5

$T_c/T_{c0}$ as a function of a normalized scattering rate $g=\hslash /2\pi k_B{T}_{c0}\tau$ in Ba${}_{1-x}$K${}_x$Fe${}_2$As${}_2$ ($x=0.23$, 0.42, and 0.69) evaluated by (a) the five-orbital model $g^{5\mathrm{orb}}=0.88z\Delta {\rho }_0/T_{c0}$, (b) the London penetration depth $g^{\lambda }=\hslash \Delta {\rho }_0/\pi k_B{T}_{c0}{\mu }_0{\lambda }^2$, and (c) the Hall coefficient $g^H=\hslash \Delta {\rho }_{0}e/\pi k_B{T}_{c0}{m}^{*}{R}_H$. These data are linearly extrapolated to obtain critical values of $g$ as shown by dotted lines. Dashed lines indicate the critical scattering rate $g_c^{\pm }\simeq 0.3$ by simple estimation for the $s_{\pm }$-wave scenario.

Figure 6

(a) A magneto-optical image at 33 K under $H=5$ Oe taken after removing silver paste and gold wire from the crystal of Ba${}_{0.6}$K${}_{0.4}$Fe${}_2$As${}_2$ shown in panel (b).