Nonexponential London penetration depth of external magnetic fields in superconducting ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2$ single crystals

We have studied the in- and out-of-plane magnetic penetration depths in the hole-doped iron-based superconductor ${\text{Ba}}_{1-x}{\text{K}}_x{\text{Fe}}_2{\text{As}}_2\left(T_c\approx 30\text{K}\right)$. Single crystals grown from different fluxes and by different groups showed nearly identical results. The in-plane London penetration depth ${\lambda }_{ab}$ is not exponentially saturating at low temperature, as would be expected from a fully gapped superconductor. Instead, ${\lambda }_{ab}\left(T\right)$ shows a power-law behavior, $\lambda \propto T^n\left(n\approx 2\right)$, down to $T\approx 0.02T_c$, similar to the electron-doped $\text{Ba}{\left({\text{Fe}}_{1-x}{\text{Co}}_x\right)}_2{\text{As}}_2$. The penetration depth anisotropy ${\gamma }_{\lambda }={\lambda }_c\left(T\right)/{\lambda }_{ab}\left(T\right)$ increases upon cooling, opposite to the trend observed in the anisotropy of the upper critical field, ${\gamma }_{\xi }=H_{c2}^{\perp c}\left(0\right)/H_{c2}^{\parallel c}\left(0\right)$. These are universal characteristics of both the electron- and hole-doped 122 systems, suggesting unconventional multigap superconductivity. The behavior of the in-plane superfluid density ${\rho }_{ab}\left(T\right)$ is discussed in light of existing theoretical models proposed for the iron pnictide superconductors.

Figure 1

(Color online) ${\lambda }_{ab}\left(T\right)$ for sample A, grown from Sn flux (Ref. 5), and for sample B, grown from FeAs self-flux (Ref. 6). Inset: temperature dependence of resistivity for each sample, normalized to the room-temperature value.

Figure 2

(Color online) Low-temperature region of ${\lambda }_{ab}\left(T\right)$ for sample A and sample B, respectively. Inset: $\Delta {\lambda }_{ab}$ vs ${\left(T/T_c\right)}^2$ for hole-doped (sample B from present work) and electron-doped ($x=0.074$ Co from Ref. 18) FeAs-122 (shifted vertically for clarity). Dashed lines represent linear fits.

Figure 3

(Color online) In-plane ${\lambda }_{ab}\left(T\right)$ and out-of-plane ${\lambda }_c\left(T\right)$ penetration depths for sample B. Inset (a): variation in temperature of ${\gamma }_{\lambda }={\lambda }_c/{\lambda }_{ab}$ obtained by dividing the values from the main panel and ${\gamma }_{\xi }\left(T\right)$ from Ref. 25. Inset (b): ${\gamma }_{\lambda }$ for hole-(current work) and electron-doped (Ref. 24) FeAs-122.

Figure 4

(Color online) (a) ${\rho }_{ab}\left(T\right)$ for ${\lambda }_{ab}\left(0\right)=180\text{nm}$ (symbols), fit with a two-gap model (continuous line), as explained in the text and theoretical calculation for $d$-wave gap symmetry (dashed lines). Inset: zoom on the low-temperature region. (b) ${\rho }_{ab}\left(T\right)$ for ${\lambda }_{ab}\left(0\right)=600\text{nm}$ (symbols) and our theoretical calculations based on the model from Ref. 31 for the following values of dimensionless impurity scattering parameters $\left({\Gamma }_0/2\pi T_{c0},{\Gamma }_{\pi }/2\pi T_{c0}\right)$ (top to bottom): (0,0.064), (3, 0.064), (3,0.068), and (3,0.060), where $T_{c0}$ is the critical temperature in the absence of impurities. Upper inset: the lowest-temperature region showing good agreement between experiment and theory. Lower inset: low-temperature region of ${\lambda }_{ab}\left(T\right)$ for sample B and the theoretical results for the same parameters as in the main panel.