Two-Gap Superconductivity in ${\mathrm{Ba}}_{1-x}{\mathbf{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$: A Complementary Study of the Magnetic Penetration Depth by Muon-Spin Rotation and Angle-Resolved Photoemission

We investigate the magnetic penetration depth $\lambda$ in superconducting ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ ($T_c\simeq 32\mathrm{K}$) with muon-spin rotation ($\mu \mathrm{SR}$) and angle-resolved photoemission (ARPES). Using $\mu \mathrm{SR}$, we find the penetration-depth anisotropy ${\gamma }_{\lambda }={\lambda }_c/{\lambda }_{ab}$ and the second-critical-field anisotropy ${\gamma }_{H_{c2}}$ to show an opposite $T$ evolution below $T_c$. This dichotomy resembles the situation in the two-gap superconductor ${\mathrm{MgB}}_2$. A two-gap scenario is also suggested by an inflection point in the in-plane penetration depth ${\lambda }_{ab}$ around 7 K. The complementarity of $\mu \mathrm{SR}$ and ARPES allows us to pinpoint the values of the two gaps and to arrive to a remarkable agreement between the two techniques concerning the full $T$ evolution of ${\lambda }_{ab}$. This provides further support for the described scenario and establishes ARPES as a tool to assess macroscopic properties of the superconducting condensate.

Figure 1

Temperature evolution of ${\sigma }_{\mathrm{sc}}$ measured after field cooling in ${\mu }_{0}H=10\mathrm{mT}$ applied in parallel (red or gray circles) and perpendicularly (blue or dark gray circles) to the crystallographic $c$ axis. The inset shows the temperature evolution of the initial TF asymmetry $A^{\mathrm{TF}}(t=0)=A_1+A_2$ (closed symbols) and the superconducting asymmetry $A_1$ (dashed lines) normalized to $A^{\mathrm{TF}}$ at $T=100\mathrm{K}$. The colored or shaded areas represent volume fractions. Note the logarithmic $T$ scale.

Figure 2

Temperature evolution of the magnetic penetration-depth anisotropy ${\gamma }_{\lambda }={\lambda }_c/{\lambda }_{ab}={\sigma }^{\parallel c}/{\sigma }^{\perp c}$. The line is a guide to the eye. In the inset we compare ${\gamma }_{\lambda }$ with the $H_{c2}$-anisotropy ${\gamma }_{H_{c2}}$ obtained for ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ by Yuan et al. [23] and Altarawneh et al. [24], albeit in samples with somewhat different $T_c$. For better comparison, $T$ is divided by the respective $T_c$ and the values of ${\gamma }_{\lambda }$ and ${\gamma }_{H_{c2}}$ are normalized to 1 for the data point closest to $T_c$.

Figure 3

Temperature evolution of the inverse squared in-plane magnetic penetration depth ${\lambda }_{ab}^{-2}$ obtained from the measured ${\sigma }^{\parallel c}$ presented in Fig. 1 by using the relation $\sigma (\mu {\mathrm{s}}^{-1})=0.1067{\lambda }^{-2}(\mu {\mathrm{m}}^{-2})$ [28]. The solid line represents the result of a fit of Eq. (6) to the $\alpha$ model, the dashed line represents a calculation of ${\lambda }_{ab}^{-2}$ from the electronic structure revealed by ARPES [29] with one fitting parameter, ${\Delta }_2$. Inset: contributions of different Fermi-surface sheets to ${\lambda }_{ab}^{-2}$. (b) Fermi surface of BKFA. (c) Temperature dependence of the SC gap, extracted from ARPES spectra [5].