Superconducting order parameter and bosonic mode in hydrogen-substituted ${\mathrm{NdFeAsO}}_{0.6}{\mathrm{H}}_{0.36}$ revealed by multiple-Andreev-reflection spectroscopy

Using intrinsic multiple-Andreev-reflection-effect spectroscopy, we studied ballistic superconductor-normal metal-superconductor (SnS) contacts in layered oxypnictide superconductors ${\mathrm{NdFeAsO}}_{0.6}{\mathrm{H}}_{0.36}$ with critical temperatures $T_c=45-48$ K. We directly determined the magnitude of two bulk superconducting order parameters, the large gap ${\mathrm{\Delta }}_L\approx 10.4$ meV, a possible small gap ${\mathrm{\Delta }}_S\approx 1.8$ meV, and their temperature dependence. Additionally, a resonant coupling with a characteristic bosonic mode was observed—the boson energy at 4.2 K, ${\varepsilon }_0=10.5-11.0$ meV being less than the indirect gap (${\mathrm{\Delta }}_L<{\varepsilon }_0<{\mathrm{\Delta }}_L+{\mathrm{\Delta }}_S$).

Figure 1

(a) Raw dynamic conductance spectra measured at $T=4.2$ K for SnS Andreev arrays with a various number of series junctions $m$. The curves were shifted vertically for clarity. (b) The same $d\mathrm{I}\left(\mathrm{V}\right)/d\mathrm{V}$ spectra with suppressed monotonic background; the bias voltage axis was normalized with corresponding $m$ ($V_{\mathrm{norm}}\equiv V_{\mathrm{array}}/m_i$). Also presented are current-voltage characteristics (left axis) for $m=5$ junction arrays. Dashed line shows simulated ohmic I(V) at $T_c$. Gray areas and $n_L=1,2,3$ labels indicate the position of subharmonic gap structure dips for the large gap ${\mathrm{\Delta }}_L\approx 10.4$ meV.

Figure 2

(a) Dynamic conductance (right axis) at $T=4.2$ K of Andreev array ($m=12$ junctions) showing two subharmonic gap structures for the large gap ${\mathrm{\Delta }}_L\approx 10.5$ meV (vertical gray lines and blue $n_L=1$, 2, 3 labels) and for the small gap ${\mathrm{\Delta }}_S\approx 1.8$ meV (arrows and $n_S$ labels). $V_{\mathrm{norm}}\equiv V_{\mathrm{array}}/12$. Monotonic background is suppressed for clarity. Current-voltage characteristic (left axis) at $T=4.2$ K and its simulation at $T_c$ (dash-dot line) are shown for comparison. (b) The low-bias fragment of the $d\mathrm{I}\left(\mathrm{V}\right)/d\mathrm{V}$ spectrum shown in (a), which details the Andreev structure of the small gap (vertical gray lines, $n_S=1$, 2, 3 labels). Monotonic background is suppressed separately for positive and negative bias. (c) The SGS positions versus their inverse number $1/n$ for the large gap (solid symbols) and the small gap (open symbols) in dI(V)/dV spectra of various Andreev arrays shown in Figs. 1–3 and 5. The data in (a), (b) panels are illustrated with red circles. Solid lines are guidelines.

Figure 3

(a) Evolution of the dynamic conductance spectrum with temperature for SnS Andreev array from Fig. 2. Dash-dot bars and $n_L=1,2,3$ labels indicate the subharmonic gap structure dips for the large gap ${\mathrm{\Delta }}_L\approx 10.5$ meV. The inset shows the low-bias fragments (with suppressed monotonic background) of the spectra shown in (a) which detail the first ($n_S=1$, up arrows) and the second ($n_S=2$, down arrows) features for the expected small gap ${\mathrm{\Delta }}_S\approx 1.8$ meV. $d\mathrm{I}\left(\mathrm{V}\right)/d\mathrm{V}$ curves are shifted vertically for clarity. (b) Temperature dependence of the first (solid symbols) and the second (open symbols) Andreev features $V_n\left(T\right)$ for the large gap (circles), and for the small gap (rhombs). Stars and crosses show how $2\times V_{n_L=2}\left(T\right)$ and $V_{n_S=1}\left(T\right)$ dependencies, respectively, correspond with $V_{n_L=1}\left(T\right)$ for the large gap SGS.

Figure 4

Temperature dependence of the superconducting gaps obtained (a) using data in the previous figure and (b) compared with other ${\mathrm{\Delta }}_L\left(T\right)$ measured with the samples from the same batch. ${\mathrm{\Delta }}_L\left(T\right)$ dependencies are shown by solid symbols, ${\mathrm{\Delta }}_S\left(T\right)$ by open circles. Theoretical fits using the two-band RBCS model are shown with solid lines (a), dash-dot line corresponds to a single-band BCS-like behavior (b). Gray dashed lines frame the confident intervals for the large and the small gap values. Resistive superconducting transition of the dense multicrystalline material is presented by gray open rhombs (right scale).

Figure 5

Dynamic conductance spectra (right scale) measured at $T=4.2$ K for Andreev arrays ($m=14$ junctions). $V_{\mathrm{norm}}\equiv V_{\mathrm{array}}/14$. Gray lines and $n_L=1-4$ labels indicate the subharmonic gap structure dips for the large gap ${\mathrm{\Delta }}_L\approx 10.3$ meV. Vertical arrows point to the fine structure dips caused by resonant emission of bosons with energy ${\varepsilon }_0=10.5-11.0$ meV. CVC at $T=4.2$ K (blue line, left scale) and its simulation at $T_c$ (dashed line) are shown for comparison; the Andreev current component is presented in the lower inset. The upper inset shows the position of gap features (circles) and fine structure (triangles) versus their inverse number. Solid lines are guidelines.

Figure 6

(a) The raw positions of the second Andreev subharmonic $V_{n_L=2}={\mathrm{\Delta }}_L/e$ in the obtained dI(V)/dV spectra versus the congruent $m$ numbers of junctions in the stack. The dash-dot line designates the BCS limit $1.76k_B{T}_c$ below which the experimental points not to be. (b) The half width of the main $n_L=1$ Andreev dips normalized to ${\mathrm{\Delta }}_L$ in dependence on the number of junctions. Solid line is a guideline. The extracted ${\mathrm{\Delta }}_L=10.45\pm 0.15$ meV values are shown in (c). For comparison, the large gap values to be obtained when the raw $V_{n_L=2}$ are normalized with other sets of $m_{\mathrm{even}}^{*}=m/2$ (gray bars), $m_{\mathrm{odd}}^{*}=m/2\pm 0.5$ (horizontally and diagonally dashed bars, respectively), $m^{+}=m+1$, and $m^{-}=m-1$, are shown in (e)–(f) panels. The bar height corresponds to the chosen $m$. (g) The main Andreev dips ($n_L=1$) observed at $2{\mathrm{\Delta }}_L/e$ bias in the representative spectra of Andreev arrays with various $m$. The $d\mathrm{I}\left(\mathrm{V}\right)/d\mathrm{V}$ curves are shifted vertically for clarity; monotonic background was suppressed.