Evidence for Two Energy Gaps in Superconducting ${\mathrm{Ba}}_{0.6}{\mathbf{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ Single Crystals and the Breakdown of the Uemura Plot

We report a detailed investigation on the lower critical field $H_{c1}$ of the superconducting ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ (122) single crystals. A pronounced kink is observed on the $H_{c1}(T)$ curve, which is attributed to the existence of two superconducting gaps. By fitting the data $H_{c1}(T)$ to the two-gap BCS model in the full temperature region, a small gap of ${\Delta }_a(0)=2.0\pm 0.3\mathrm{meV}$ and a large gap of ${\Delta }_b(0)=8.9\pm 0.4\mathrm{meV}$ are obtained. The in-plane penetration depth ${\lambda }_{ab}(0)$ is estimated to be 105 nm corresponding to a rather large superfluid density, which points to the breakdown of the Uemura plot in 122 superconductors.

Figure 1

(a) X-ray diffraction pattern of the ${\mathrm{Ba}}_{0.6}{\mathrm{K}}_{0.4}{\mathrm{Fe}}_2{\mathrm{As}}_2$ crystal. The right inset shows the sample (No. 1) under the optical microscope. The scale underneath with $100\mu \mathrm{m}/\mathrm{\text{grid}}$ is used to display the size of the sample. The left inset shows the resistive transition on one crystal cut from the same piece. (b) The induction $B$ by Hall probe as a function of $T$ measured in zero-field-cooled mode. Inset: A typical magnetization hysteresis loop measured at 32.1 K by the Hall sensor.

Figure 2

(a) A typical magnetization hysteresis loop (symbols), the solid lines are the linear fitting curves using the low field data (Meissner line). The increasing and decreasing branches are shifted downward and upward, respectively, for clarity. The same case is shown in the bottom-left inset when the maximum field is less than $H_{c1}$. The upper-right inset shows the magnetization data subtracted by the Meissner line. The arrows indicate the direction of sweeping fields and the determination of $H_{c1}$. (b) The initial part of the magnetization curves $M(H)$ of sample No. 2 at various temperatures. The dashed line gives the Meissner linear approach. Inset: The same magnetization data in field subtracted by the Meissner line. The dashed line in the inset sets up a criterion of 0.5 Oe.

Figure 3

The extracted $H_{c1}$ as a function of $T$ for sample No. 1 (a) and No. 2 (b) (full circles with error bars). The open dotted circles in (b) represent the $H_{c1}$ determined from the vibrating sample magnetometry measurements taken into account of the demagnetization effect. The solid lines are the fitting curves using the two-gap model. The contributions of the small gap $[H_{c1}({\Delta }_a)]$ and the large gap $[H_{c1}({\Delta }_b)]$ in the model are also shown by the dotted and dashed lines, respectively. The two insets in (a) and (b) show the enlarged views of the data $H_{c1}(T)$ in low temperature region together with the theoretical fitting curves (solid lines).

Figure 4

The correlations between $T_c$ and the superfluid density $n_s/m^{*}$. Points for the cuprates are taken from Ref. 17. The full triangles show the data for F-LaFeAsO (Ref. [3, 17]) and F-SmFeAsO (Ref. [10] and our work). The data of ${\mathrm{MgB}}_2$ and ${\mathrm{NbSe}}_2$ are taken from Ref. 21, 30, respectively.