Spin-split superconductivity in spin-orbit coupled hybrid nanowires with ferromagnetic barriers

Abstract

We report transport studies of hybrid Josephson junctions based on semiconducting InAs nanowires with fully overlapping epitaxial ferromagnetic insulator EuS and superconducting Al partial shells. Current-biased measurements reveal a hysteretic superconducting window with a sizable supercurrent near the coercive field of the ferromagnetic insulator, accompanied by multiple Andreev reflections. Tunneling spectroscopy shows a superconducting gap characterized by three peaks, which we attribute to tunneling between exchange-split superconductors. A theoretical model reproduces the observed features and indicates that spin mixing, driven by sizable spin-orbit coupling, is essential to their formation. Our results demonstrate proximity-induced superconductivity through a ferromagnetic insulator and establish a new platform for exploring spin-triplet pairing.

Figures (5)

• Figure 1: (a) Schematic of a hexagonal InAs nanowire showing EuS and Al shells fully overlapping on two facets. (b) Scanning electron micrograph of nanowire after selective junction etching with enhanced false coloration of different materials. (c) Colorized micrograph of a representative Josephson junction device with the measurement setup. (d) and (e) Differential resistance, $R$, as a function of current bias, $I$, and parallel magnetic field, $H$, for junction 1 sweeping $H$ from (d) negative to positive and (e) positive to negative. Data were taken at $V_\mathrm{BG} = 0$ and $V_\mathrm{JG} = 0$.
• Figure 2: (a) Differential resistance, $R$, as function of measured voltage drop, $V$, across the junction, taken from the data in Fig. \ref{['fig:1']} at $\mu_0 H = -20$ mT. A series of peaks in $R$ appear at finite $V$, corresponding to multiple Andreev reflections of order $n$. (b) Peak positions scale linearly with $1/n$. A linear fit to the expected relation, $V = 2\Delta/en$, yields an induced superconducting gap of $\Delta = 60~\mu$eV.
• Figure 3: (a) Differential conductance, $dI/dV$, for junction 1 as a function of source-drain voltage bias, $V$, and junction gate voltage, $V_\mathrm{JG}$, displaying the evolution from weak-tunneling to the open regime. Data were taken at $V_\mathrm{BG} = -6.5$ V, $\mu_0 H = -20$ mT. (b) Tunneling $dI/dV$ as a function of $V$ and decreasing parallel magnetic field, $H$, revealing a gapped spectrum with a triple-peak structure between $\mu_0 H = -15$ and $-30$ mT. (c) Line cut from (a) in the open regime at $V_\mathrm{JG} = -1.663$ V, showing a supercurrent peak at zero bias and multiple Andreev reflection features at $V=\pm\Delta$ and $\pm2\Delta$. (d) Similar to (c) but taken in the tunneling regime at $V_\mathrm{JG} = -1.666$ V, showing a gap with three well-resolved peaks. The central peak corresponds to $2\Delta = 130~\mu$V and is symmetrically flanked by side peaks, indicating spin splitting of $h = 40~\mu$eV.
• Figure 4: (a) Schematic of the model junction consisting of two superconducting (SC) leads with pairing potential $\Delta_0$, tunnel-coupled to normal conductor (NC) through ferromagnetic insulator (FI) barrier parametrized by $\gamma_b^{\rm FI}$. The NC has an induced gap $\Delta$, exchange field $h$, and dimensionless spin–orbit coupling parameter $\alpha = m\alpha_{\rm R} \xi$, where $\alpha_{\rm R}$ is the Rashba coefficient, $m$ the effective mass, and $\xi$ the superconducting coherence length. The junction barrier is characterized by $\gamma_b^{\rm J}$. (b) Local density of states, LDOS, at the junction barrier for $\alpha = 0$, showing spin-split coherence peaks due to $h$, with spin-polarized (spin-degenerate) states below (above) $\Delta$. (c) Same as (b), but for $\alpha = 0.3$, with both spin components present at all energies due to spin mixing. (d) Schematic of resonant tunneling processes enabled by spin mixing due to finite $\alpha$. Note that for $\alpha = 0$, only the $2\Delta$ process is allowed. (e) Calculated differential conductance, $G$, in units of normal-state barrier conductance, $G_{\rm B}$, as a function of voltage bias, $V$, for increasing $\alpha$, showing the emergence of the triple-peak structure. Curves are offset vertically for clarity. Further computational details are provided in Ref. Supplement.
• Figure 5: (a) Tunneling conductance, $dI/dV$, as a function of voltage bias, $V$, taken for junction 1 at several parallel magnetic field values, $H$, at back-gate voltage $\textit{V}_\mathrm{BG} = -6.5$ V, displaying a relatively hard gap with three well-resolved peaks. (b) Same as (a) but taken at $\textit{V}_\mathrm{BG} = 0$, showing a softer gap and the inner peaks partially merging with the central peak, consistent with enhanced spin-orbit coupling (see main text).