Coherent subgap transport in spin-split Josephson junctions

Abstract

We report the first experimental observation of subgap transport in ferromagnetic insulator/superconductor/insulator/superconductor junctions realized in EuS/Al/AlOx/Al vertical stacks. Differential conductance measurements reveal multiple Andreev reflection peaks, with odd-order peaks split by the spin-splitting induced in the superconductor adjacent to EuS, while even-order peaks remain unaffected. Combining experiments with quasiclassical transport modeling, we extract the spin-splitting and the distribution of transmission channels, finding that a significant fraction ($\sim 23\%$) of highly transparent channels ($τ\approx 0.9$) dominates transport. The observation of a Josephson current further confirms strong superconducting coupling through these channels. Our results demonstrate that a single spin-split superconductor is sufficient to observe the even-odd MAR effect. Our work establishes EuS/Al junctions as a versatile platform to study subgap transport, Josephson coupling, and spin-polarized superconducting phenomena.

Figures (6)

• Figure 1: (a) Device and geometry description. The $12\;\text{nm}$ bottom Al (S1) strip sits on top of the continuous $12\;\text{nm}$ EuS bottom layer (FI). We perform tunneling spectroscopy across the oxide barrier (I) using the $20\;\text{nm}$ top Al (S2) as the second electrode. (b) Density of states of a BCS non-split (S2) and spin-split (S1) superconductors separated by a barrier with no applied bias voltage. The exchange interaction splits the density of states by $h$
• Figure 2: (a) Tunneling spectroscopy of three diferent devices at zero field and $10\;\text{mK}$. The curves are displaced vertically for clarity. (b) Schematics of the $n=2$ MAR process, where a charge transfer of $2e$ happens between the electrodes. (c) [(d)] Temperature dependance of the experimental data [simulations] from the purple curve in panel (a). Dashed black and brown lines mark the $10$ and $300\;\text{mK}$ linecuts showed in (e) and (f). A zoom at the black square is shown to highlight the difference between the QP peak and the MAR peak (blue arrows). (e), (f) Linecut comparison between data and model at $10\;\text{mK}$ and $300\;\text{mK}$.
• Figure 3: Theoretical predictions of the higher MAR orders.(a) Numerical simulation of the tunneling conductance as a function of the barrier transparency for $\tau=0.3$, $0.6$ and $0.9$. The rest of the parameters are fixed at $\Delta_1=220\;\mu\text{eV}$, $\Delta_2=190\;\mu\text{eV}$, $h=55\;\mu\text{eV}$ and $\tau_{\mathrm{sf}}=(0.02\Delta_{0})^{-1}$. Higher transmission resolve higher MAR orders while broadening the outer features. (b) and (c) Schematics of a $n=3$ MAR process for the two spin selection possibilities (blue, green). This odd order transfers three charges which creates the spin-split resonance.
• Figure 4: Full characterization of the device with lower interface resistance. (a) Tunneling conductance (blue) and simulations (red) at $30\;\text{mK}$. Vertical line cuts show the different MAR orders, odd spin-split (blue-green) and even not spin-split (black). (b) [(c)] Temperature dependence of the tunneling conductance from the experiment [simulations]. Features decay to smaller energies as $T \to T_{c}$. (d) and (e) Josephson critical current measured (blue) from the IV curves (inset in (e)), modified Ambegaokar-Baratoff prediction (Eq. \ref{['eq:AGIc']}, red) and going beyond the tunneling limit (Eq. \ref{['eq:FullIc']}, green) against the temperature and magnetic field of the system. The inset in panel (e) shows the measured IV around 0. $I_c=\text{max}(I[E=0])$
• Figure 5: Experimental measurement of $R(T)$ for different samples. 2 samples shown in Fig. \ref{['fig:2']}(a), purple curve labeled as $h_{1}=100\;\mu\text{eV}$, and the orange curve, labeled as $h_{2}=75\;\mu\text{eV}$; and the sample shown in Fig. \ref{['fig:4']}(b), labeled as $h_{3}=55\;\mu\text{eV}$. The blue curve refers to the $12\;\text{nm}$ bottom, non-proximitized Al that serves as $T_{C0}$ in Eq. \ref{['eq:TcFormula']}. The red curve is the top $20\;\text{nm}$ Al, which is supposed to be the same for every sample for simplicity. Data is normalized to the resistance on the normal state $R_{T_{N}}$