Lower critical field and SNS-Andreev spectroscopy of 122-arsenides: Evidence of nodeless superconducting gap

Using two experimental techniques, we studied single crystals of the 122-FeAs family with almost the same critical temperature, $T_c$. We investigated the temperature dependence of the lower critical field $H_{c1}\left(T\right)$ of a ${\mathrm{Ca}}_{0.32}{\mathrm{Na}}_{0.68}{\mathrm{Fe}}_2{\mathrm{As}}_2$ $(T_c\approx 34\text{K})$ single crystal under static magnetic fields $H$ parallel to the $c$ axis. The temperature dependence of the London penetration depth can be described equally well either by a single anisotropic $s$-wave-like gap or by a two-gap model, while a $d$-wave approach cannot be used to fit the London penetration depth data. Intrinsic multiple Andreev reflection effect spectroscopy was used to detect bulk gap values in single crystals of the intimate compound ${\mathrm{Ba}}_{0.65}{\mathrm{K}}_{0.35}{\mathrm{Fe}}_2{\mathrm{As}}_2$, with the same $T_c$. We estimated the range of the large gap value ${\Delta }_L=6–8$ meV (depending on small variation of $T_c)$ and its a $k$ space anisotropy of about 30%, and the small gap ${\Delta }_S\approx 1.7\pm 0.3$ meV. This clearly indicates that the gap structure of our investigated systems more likely corresponds to a nodeless $s$-wave two gaps.

Figure 1

Top: Magnetic-field dependence of the isothermal magnetization $M$ vs $H$ loops measured at different temperatures ranging from 2 to 12 K up to 45 kOe, with the field parallel to the $c$ axis, for a ${\mathrm{Ca}}_{0.32}{\mathrm{Na}}_{0.68}{\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystal. Inset: Temperature dependence of the zero-field-cooled magnetic susceptibility $\chi$ after demagnetization correction in an external field of 10 Oe applied along $c$. Bottom: Initial part of the magnetization curves measured at various temperatures for $H\parallel c$. Inset: An example used to determine the $H_{c1}$ value using the regression factor $R$ at $T=2$ K.

Figure 2

Critical current density $J_c$ at various temperatures up to 45 kOe for $H\parallel c$. Inset: Temperature dependence of the $J_c$ values at $H=0$ for a ${\mathrm{Ca}}_{0.32}{\mathrm{Na}}_{0.68}{\mathrm{Fe}}_2{\mathrm{As}}_2$ single crystal. The line is a guide for the eyes. The error bar at $T=2$ K shows the uncertainty of the estimated value due to the irregular jumps close to $H=0$.

Figure 3

Temperature dependence of $H_{c1}$ vs temperature for a field applied parallel to the $c$ axis. $H_{c1}$ has been estimated from the regression factor (see inset in Fig. 2, bottom). Bars show the uncertainty estimated by the deviating point of the regression fits. Inset: Scaling of the lower critical field values of ${\mathrm{Ca}}_{0.32}{\mathrm{Na}}_{0.68}{\mathrm{Fe}}_2{\mathrm{As}}_2$ together with various Fe-based, ${\mathrm{MgB}}_2$, and cuprate superconductors (see text).

Figure 4

Plots showing the fitting of theoretical curves (by the method described in the text) to experimental data on the temperature dependence of ${\lambda }_{ab}^{-2}$ calculated using $H_{c1}$ for a field applied parallel to the $c$ axis. The fits to the experimental data are shown as solid lines for (a) a single $s$ wave (BCS fit), (b) a $d$ wave, (c) an anisotropic $s$ wave, and (d) a two-gap $s$-wave. Also, in (d), the two solid lines represent the contribution by gaps ${\Delta }_1\left(0\right)$ and ${\Delta }_2\left(0\right)$ to the fitting of ${\lambda }_{ab}^{-2}$.

Figure 5

Current-voltage characteristics I(V) and dynamic conductance spectra $dI\left(V\right)/dV$ for SNS-Andreev array d realized on a Ba4 sample (two junctions in the stack). The bias voltage is scaled down by a factor of 2, correspondingly. Data were obtained at $T=5.3$ K. The local critical temperature of the contact point is about $34\pm 1$ K. The dashed line is the linear dependence, plotted for comparison. The (blue) $n_L$ labels with arrows indicate the subharmonic gap structure. Upper inset: Experimental ${\Delta }_L\left(T\right)$ data (circles). The solid line is BCS-like dependence. Lower inset: Bias voltages $V_n$ for the $n_L$ series of dips versus their inverse ordinary numbers. Note that the $V_n(1/n)$ dependence (line), as expected, passes through the origin, for ${\Delta }_L\approx 8.0$ meV.

Figure 6

Current-voltage characteristics I(V) (thin) and their dynamic conductance spectra $dI\left(V\right)/dV$ (thick lines) for two SNS-Andreev arrays, 5 and b, realized in Ba6 and Ba4 samples from the same batch. Since there are two junctions in the stack, the bias voltage is scaled down by a factor of 2, $T=4.2$ K. The local critical temperature of the contact point is about $34\pm 3$ K. Dashed linear dependencies, crossing the origin, are plotted for comparison. The (blue) $n_L$ labels and arrows indicate the subharmonic gap structure (SGS) of ${\Delta }_L$; black labels and vertical bars, the SGS of ${\Delta }_S\approx 1.7\pm 0.3$ meV. ${\Delta }_L\approx 5.5$–7.4 meV, the width of the Andreev minima, is determined by the $k$-space anisotropy of about 30% and represented by the marker lines. Monotonic background of conductance spectra is subtracted.