Influence of the Fermi surface geometry on the Josephson effect between iron-pnictide and conventional superconductors

We study hybrid Josephson junctions between a multiband ${\mathrm{Ba}}_{1-x}{\mathrm{Na}}_x{\mathrm{Fe}}_2{\mathrm{As}}_2$ iron-pnictide and Nb. We observe that the insertion of a Cu interlayer in such junctions leads to a dramatic enhancement of the $I_c{R}_n$ product, despite the weaker proximity-induced superconductivity of Cu. This counterintuitive phenomenon is attributed to the differences in Fermi surface geometries of Nb and Cu, which affect the selectivity of tunneling in sign-reversal $s_{\pm }$ bands of pnictide. Our results indicate that the sensitivity to Fermi surface geometries provides a new tool for phase-sensitive studies and paves the way to conscious Fermi surface engineering of pnictide junctions.

Figure 1

(a) SEM image of a BNFA-Cu/Nb sample (painted). (b) Sketch of the sample. Junctions are formed at a freshly cleaved surface of the crystal in the area at the overlap between a window-line opening in $\mathrm{Si}{\mathrm{O}}_2$ and the top Nb electrodes. (c) Resistive transitions of a junction (J2; red line) and BNFA crystal (blue line) for the BNFA-Cu/Nb sample. (d), (e) $I-V$ curves at different temperatures and $H=0$ for junctions at BNFA-Nb (d) and BNFA-Cu/Nb (e) samples. The wine-colored curve in (e) represents $I-V$ at $T\simeq 0.3$ K and $H_{\parallel }=15$ mT. It demonstrates the complete suppression of $I_c$ by a modest in-plane magnetic field. (f) Temperature dependencies of normal resistances for BNFA-Nb (red line) and BNFA-Cu/Nb (blue line) junctions.

Figure 2

(a) Modulation of the critical current versus the in-plane magnetic field for a BNFA-Cu/Nb junction at different temperatures. (b) Comparison of $I_c$ versus flux modulation patterns of BNFA-Cu/Nb (red line) and BNFA-Nb (blue line) and the Fraunhofer pattern (black line). (c) $I-V$ characteristics of a BNFA-Cu/Nb junction with (red line) and without (black line) microwave radiation. The primary Shapiro step is clearly shown. (d) Differential conductance versus inverse voltage, demonstrating the presence of subharmonic Shapiro steps. (e) Temperature dependencies of critical current densities of BNFA-Cu/Nb (blue line; left scale) and BNFA-Nb (red line; right scale) junctions. (f) Temperature dependencies of $I_c{R}_n$ products for the same junctions. Note the big difference in $I_c{R}_n$ values. The dotted black line represents a normalized theoretical curve for conventional $s$-wave superconductors [4]. The dashed black line shows a simulated dependence for an $s-s_{\pm }$ junction from Ref. [8].

Figure 3

Fermi surface topologies in the first Brillouin zone for (a) Cu, (b) Nb, and (c) BNFA. $k_z$-integrated projections of densities of states on the (001) plane for (d) Cu and (e) Nb. Similar averaged DoS projections for polycrystalline (f) Cu and (g) Nb films. Products of DoS projections of monocrystalline BNFA with polycrystalline (h) Cu and (i) Nb. It can be seen that for BNFA-Cu junctions (h) the tunneling current flows predominantly into the corner propellerlike bands of BNFA. On the other hand, for BNFA-Nb junctions (i) it is distributed relatively uniformly between central and corner bands.

Figure 4

SEM images of BNFA-Cu/Nb samples. (a) The original (unpainted) image from Fig. 1. (b) Closeup view of the junction.

Figure 5

BNFA sample characterization. (a) SEM image of a BNFA-Nb sample with a typical multiterminal configuration for in-plane ($\mathrm{Vin}+$ $\mathrm{Vin}-$) and junction J2 and J5 ($\mathrm{V2}+$, $\mathrm{V2}-$ and $\mathrm{V5}-$, $\mathrm{V5}+$) measurement. $\mathrm{I}+$ and $\mathrm{I}-$ are current connections. (b) A sapphire ($5\times 5\mathrm{mm}$) substrate with a BNFA crystal and electrodes is glued and bonded to PCB. Inset: Sample holder with PCB. (c) Fraunhofer modulation $I_c\left(H\right)$ for all BNFA-Nb/Cu junctions at 3.6 K. (d) The Fraunhofer modulation of positive and negative critical currents $I_c\left(H\right)$. Inset: Magnetic field of the maximum and the minimum positions. (e) $I-V$ curves of BNFA-Nb/Cu junctions J1–J5 in a microwave field (73.6 GHz).

Figure 6

Radial momentum distributions of $k_z$-integrated projections of Fermi surfaces on the (001) plane for Cu (solid red curve) and Nb (dashed blue curve) averaged over the in-plane momentum angle. These profiles represent the effective density-of-states distribution for polycrystalline Cu and Nb films.

Figure 7

Numerical simulation of $I_c{R}_n$ in Nb-BNFA junctions. (a) Temperature dependencies of energy gaps. (b) Blue and red lines represent $I_{c1}{R}_{n1}$ and $I_{c2}{R}_{n2}$ for tunneling from $s$ in each of the two bands of BNFA. For comparison, the black line shows $I_c{R}_n$ for a symmetric $s-s$ Nb-Nb junction. (c), (d) Temperature dependencies $I_c{R}_n\left(T\right)$ for different relative transparencies of the two channels, $\alpha =R_{n1}/R_{n2}\in [0,\infty ]$, for sign-conserving $s-s_{++}$ (c) and sign-reversal $s-s_{\pm }$ (d) junctions. (e) $I_c{R}_n\left(T\right)$ for different $R_{n1}/R_{n2}$ values in sign-reversal $s-s_{\pm }$ junctions close to the cancellation point. (f) Experimentally measurable absolute values of $|I_c{R}_n\left(T\right)|$ for the $s-s_{\pm }$ case close to the cancellation point. Note that dramatic amplitude and shape variations of $I_c{R}_n\left(T\right)$ occur only in the sign-reversal $s_{\pm }$ cases (d)–(f) and do not happen in the sign-conserving $s_{++}$ case (c).