Josephson current in Fe-based superconducting junctions: Theory and experiment

We present a theory of the dc Josephson effect in contacts between Fe-based and spin-singlet $s$-wave superconductors. The method is based on the calculation of temperature Green's function in the junction within the tight-binding model. We calculate the phase dependencies of the Josephson current for different orientations of the junction relative to the crystallographic axes of Fe-based superconductor. Further, we consider the dependence of the Josephson current on the thickness of an insulating layer and on temperature. Experimental data for ${\mathrm{PbIn}/\mathrm{Ba}}_{1-x}{\mathrm{K}}_x({\mathrm{FeAs})}_2$ point-contact Josephson junctions are consistent with theoretical predictions for $s_{\pm }$ symmetry of an order parameter in this material. The proposed method can be further applied to calculations of the dc Josephson current in contacts with other new unconventional multiorbital superconductors, such as ${\mathrm{Sr}}_2{\mathrm{RuO}}_4$ and the superconducting topological insulator ${\mathrm{Cu}}_x{\mathrm{Bi}}_2{\mathrm{Se}}_3$.

Figure 1

Schematic illustration of 1D model of the S/I/S Josephson junction.

Figure 2

2D tight-binding model of the (100) oriented ${\text{S/I/S}}_p$ junction.

Figure 3

Fermi surfaces of the ${\text{S/I/S}}_p$ junction with a (100) oriented FeBS. (a) Fermi surface of a single-orbital s-wave superconductor and (b) Fermi surface of a FeBS.

Figure 4

3D tight-binding model for an ${\text{S/I/S}}_p$ junction along the $z$ axis. $t^{\prime },t$, and $t_z$ are hopping integrals along the $z$ axis in S, I, and ${\mathrm{S}}_p$, respectively. $\gamma$ is the hopping integral at the S/I boundary. ${\gamma }_{1z}$ and ${\gamma }_{2z}$ are hopping parameters between I and ${\mathrm{S}}_p$ for $xz$ and $yz$ orbitals, respectively.

Figure 5

The CPR for the (100) oriented ${\text{S/I/S}}_p$ junction for ${\gamma }_1=0.02,{\gamma }_2=0.2$, and $T/T_c^s\approx 0.02$. The solid line corresponds to the total Josephson current and the dotted line corresponds to the contribution from $|k_y|<\pi /2$. The line with crosses shows the contribution from $|k_y|>\pi /2$. $I_0=e{\mathrm{\Delta }}_0{L}^{\prime }/2\pi \hslash$. (a) corresponds to the direct contact and (b) corresponds to $N=3$ atomic layers in the insulating region.

Figure 6

The same as in Fig. 5, but ${\gamma }_1=0.02\text{and}{\gamma }_2=0.3$.

Figure 7

The same as in Fig. 5, but ${\gamma }_1=0.02\text{and}{\gamma }_2=0.4$.

Figure 8

The same as in Fig. 5, but ${\gamma }_1=0.2\text{and}{\gamma }_2=0.02$.

Figure 9

The ratio of the second and the first harmonics of the CPR for the (100) oriented ${\text{S/I/S}}_p$ Josephson junction for the direct contact case as a function of hopping parameters across the boundary.

Figure 10

The CPR of the ${\text{S/I/S}}_p$ Josephson junction with transport in $z$ direction for (a) the direct contact ${\text{I/S}}_p$ and (b) $N=3$ layers of an insulator atoms.

Figure 11

The temperature dependence of the maximum Josephson current of the (100) oriented ${\text{S/I/S}}_p$ junction for zero misorientation angle with respect to the interface. The solid line corresponds to the direct contact and the line with crosses corresponds to $N=3$ insulator layers. The dashed line corresponds to the Ambegaokar-Baratoff temperature dependence of the maximum Josephson current in a conventional S/I/S junction; (a) ${\gamma }_1=0.02,{\gamma }_2=0.2$; (b) ${\gamma }_1=0.02,{\gamma }_2=0.3$; (c) ${\gamma }_1=0.02,{\gamma }_2=0.4$; and (d) ${\gamma }_1=0.2,{\gamma }_2=0.02$.

Figure 12

Normalized resistance $R/R$(300 K) of the ${\mathrm{Ba}}_{0.4}{\mathrm{K}}_{0.6}({\mathrm{FeAs})}_2$ single crystals. (Upper inset) Zero-field cooled magnetization measurement. (Lower inset) Phase diagram of ${\mathrm{Ba}}_{1-x}{\mathrm{K}}_x({\mathrm{FeAs})}_2$ [45, 46]. The blue symbol represents the samples studied in this work. $T_c$ has been determined from the magnetization curve shown in the upper inset.

Figure 13

${\mathrm{Pb}}_{0.7}{\mathrm{In}}_{0.3}/{\mathrm{Ba}}_{0.4}{\mathrm{K}}_{0.6}({\mathrm{FeAs})}_2$ point-contact junctions with current injection along the $c$ axis. (a) Normalized critical current as a function of the square root of the power; (inset) subset of $I\text{−}V$ curves at $T=1.76$ K irradiated with a 6.15-GHz rf frequency at different power levels. (b) Normalized amplitude of step 1 vs (rf ${\mathrm{power})}^{1/2}$; (inset) normalized amplitude of step 2 vs (rf ${\mathrm{power})}^{1/2}$.

Figure 14

${\mathrm{Pb}}_{0.7}{\mathrm{In}}_{0.3}/{\mathrm{Ba}}_{0.4}{\mathrm{K}}_{0.6}({\mathrm{FeAs})}_2$ point-contact junctions with current injection along the $ab$ plane. (a) Normalized critical current as a function of the square root of the power; (inset) subset of $I\text{−}V$ curves at $T=1.8$ K irradiated with a 3.37-GHz rf frequency at different power levels. (b) Normalized amplitude of step 1 vs (rf ${\mathrm{power})}^{1\text{/}2}$; (inset) normalized amplitude of step 1/2 vs (rf ${\mathrm{power})}^{1/2}$.