Intrinsic Multiple Andreev Reflections in layered Th-doped Sm$_{1-x}$Th$_x$OFeAs

Abstract: Layered oxypnictide Sm$_{1-x}$Th$_x$OFeAs (Sm-1111) is an ideal candidate to be probed by intrinsic multiple Andreev reflections effect (IMARE) spectroscopy. Using the classical "break-junction" technique, we formed ballistic Andreev arrays of identical S--n--S-contacts, where $S$ is superconductor, and $n$ is a layer of normal metal. For $T < T_C$, the I(V) curve shows an excess-current and a subharmonic gap structure (SGS): a set of sharp dI(V)/dV-dips at positions which depend on the superconducting gap value, the number of junctions in the array, and the natural subharmonic order, thus manifesting the effect of intrinsic multiple Andreev reflections. Here we present the I(V) and dI(V)/dV with up to 4 SGS dips for Andreev arrays formed in optimally doped Sm-1111 with critical temperatures $T_C \approx 49$\,K, as well as in underdoped samples with $T_C \approx 37$\,K. We show that a number of Andreev subharmonics facilitates the determination of the superconducting gap with a better accuracy.

• The paper identifies robust subharmonic gap structures via IMARE spectroscopy that confirm multigap superconductivity in Th-doped Sm-1111.
• Reliable gap evaluations were achieved by normalizing subharmonic positions, yielding a large gap exceeding weak-coupling BCS limits and a detectable small gap.
• Analysis using Moskalenko–Suhl equations revealed strong interband coupling and non-BCS temperature dependence, highlighting the multiband nature of superconductivity.

Intrinsic Multiple Andreev Reflections and Multigap Superconductivity in Layered Th-doped Sm$_{1-x}$Th$_x$OFeAs

Introduction

The article presents a detailed investigation into the superconducting gap structure of Th-doped Sm$_{1-x}$Th$_x$OFeAs (Sm-1111) using intrinsic multiple Andreev reflections effect (IMARE) spectroscopy. By leveraging the break-junction technique, the authors form ballistic S–n–S arrays and probe both optimally doped and underdoped samples, uncovering robust subharmonic gap structures associated with the multi-gap superconductivity characteristic of iron-based oxypnictides.

Experimental Technique and Methodology

IMARE spectroscopy was implemented via mechanically induced break-junctions on polycrystalline Sm-1111 with Th-doping at various concentrations. The layering inherent in Sm-1111 enables the formation of intrinsic S–n–S arrays, where the normal (n) barrier layer derives from non-superconducting Sm(Th)–O spacers. For each junction stack, current-voltage ($I$–$V$) and dynamic conductance ($dI/dV$) characteristics were measured at low temperatures, with sample cooling to 4.2 K.

A key methodological strength lies in the normalization procedure by the number of effective junctions $m$ in each stack, which is essential for precise gap evaluation using the observed positions of subharmonic gap structure (SGS) dips: for each subharmonic order $n$, the dip scales as $V_n = 2\Delta / en \times m$, where $\Delta$ is the superconducting gap.

Main Results

Large and Small Gap Determination

In both optimally doped ($T_C \approx 49$ K) and underdoped ($T_C \approx 37$ K) samples, dynamic conductance spectra consistently exhibit clear SGS for the large gap with up to four subharmonics visible. For optimal doping, the large gap is unambiguously resolved with $\Delta_L = 11.8 \pm 1.2$ meV, yielding a BCS ratio $2\Delta_L / k_B T_C \approx 5.6$, which notably exceeds the weak-coupling BCS limit. In underdoped samples, up to $m=42$ junctions are inferred, with $\Delta_L = 8.3 \pm 0.6$ meV.

The signature of a smaller gap is weak, consistent with the dominance of the hole band contribution to ballistic conductance due to electron band flattening near the Fermi level. Nevertheless, the small gap $\Delta_S \approx 2.8$ meV is occasionally observable. The data further establish a gap ratio $\Delta_L / \Delta_S \approx 4.2$, in close agreement with multiband pairing theory predictions and previous ARPES studies.

Temperature Dependence and Multiband Effects

The temperature dependences $\Delta_L(T)$ and (inferred) $\Delta_S(T)$ deviate significantly from single-band BCS behavior, bending below the canonical BCS curve. This is quantitatively explained by solving Moskalenko–Suhl equations for multiband superconductors, confirming a strong interband coupling regime typical of the 1111 family. Calculations using empirical coupling matrix elements $\lambda_{ij}$ ($$\lambda_{LL}:\lambda_{SS}:\lambda_{LS}:\lambda_{SL} = 1:0.7:0.2:0.02$$) reproduce the experimental $\Delta_L(T)$ and suggest that the small gap's temperature dependence features a marked initial reduction and subsequent gradual suppression near $T_C$.

Implications and Discussion

The ability of IMARE spectroscopy in break-junction Andreev arrays to resolve multiple SGS dips with high fidelity directly supports the presence of multigap superconductivity in Sm-1111 with Th-doping. The strong-coupling BCS ratios, the alignment with ARPES-inferred gap values, and the scaling with stack size $m$ establish the robustness of the technique for bulk-sensitive superconducting gap measurement even in polycrystalline layered materials.

These results reinforce the multi-condensate nature of SC in the iron 1111 pnictides, with a dominant large gap residing on hole-like Fermi surface sheets and a smaller, less pronounced gap associated with singular electron pockets of reduced carrier concentration but substantial density of states. The observed deviation from BCS-like $T$-dependence is a diagnostic for multiband coupling and highlights the necessity of non-trivial interband pairing to explain the condensed matter properties of Fe-based high-$T_C$ superconductors.

Practically, this multigap feature and its bulk spectroscopic visibility imply possibilities for tuning $T_C$ and gap anisotropy via controlled doping or strain, potentially informing device concepts where interband coupling or gap engineering can be exploited. Furthermore, from a theoretical standpoint, the confirmation of scale-invariant gap ratios and coupling constants over a broad $T_C$ range enables comparative studies across the iron pnictide family and benchmarking of advanced Eliashberg or beyond-Migdal-Eliashberg multiband models.

Conclusion

This study demonstrates that IMARE spectroscopy via intrinsic break-junction arrays yields precise bulk gap values and scalable multigap characteristics in Th-doped Sm$_{1-x}$Th$_x$OFeAs. The large gap is accurately determined, while features attributable to the smaller gap are consistent with ARPES and theoretical expectations. The work consolidates multiband superconductivity as a defining feature of the 1111 oxypnictides and provides a framework for further investigations into the interplay of Fermi surface topology, interband coupling, and superconducting order parameter structure in layered high-$T_C$ systems.