Enhancement of proximity-induced superconductivity in a planar Ge hole gas

Hole gases in planar germanium can have high mobilities in combination with strong spin-orbit interaction and electrically tunable $g$ factors, and are therefore emerging as a promising platform for creating hybrid superconductor-semiconductor devices. A key challenge towards hybrid Ge-based quantum technologies is the design of high-quality interfaces and superconducting contacts that are robust against magnetic fields. In this work, by combining the assets of aluminum, which provides good contact to the Ge, and niobium, which has a significant superconducting gap, we demonstrate highly transparent low-disordered JoFETs with relatively large $I_{\text{C}}{R}_{\text{N}}$ products that are capable of withstanding high magnetic fields. We furthermore demonstrate the ability of phase-biasing individual JoFETs, opening up an avenue to explore topological superconductivity in planar Ge. The persistence of superconductivity in the reported hybrid devices beyond 1.8 T paves the way towards integrating spin qubits and proximity-induced superconductivity on the same chip.

Figure 1

(a) False-colored SEM of a Ge JoFET with a top gate (yellow) accumulating a 2DHG between the two superconducting electrodes (blue). The scale bar is $500\mathrm{nm}$. (b) HAADF-STEM image of the cross section of the JoFET with the Al layer directly contacting the Ge QW. The scale bar is $100\mathrm{nm}$. (c) $V$ measured across the JoFET versus $V_{\text{G}}$ and $I$. The device can be fully switched off at more positive voltages. (d) $V$ versus $I$ traces, extracted from (c), highlighting the switching current at different $V_{\text{G}}$. (e) Dependence of the $I_{\text{C}}{R}_{\text{N}}$ product on $V_{\text{G}}$ as extracted from (c).

Figure 2

(a) Differential resistance $dV/dI$ versus voltage $V$ at $T=$ 20 mK and $B=$ 0 T, showing MAR peaks up to fifth order. The inset shows the higher order MAR features observed at lower values of $V$. (b) Measured temperature dependence of the critical current $I_{\text{C}}$ for various top gate voltages $V_{\text{G}}$ (solid points, measurement error is indicated by the shaded regions). The lines present theoretical curves for a short junction [28]; the solid lines assume a ballistic junction, the dashed line a diffusive junction (scaled to best match the data for $V_{\mathrm{G}}=-2.5\mathrm{V}$.

Figure 3

(a) Differential resistance $dV/dI$ versus perpendicular magnetic field $B_{\perp }$ and voltage $V$ measured over the junction. The overlying line traces show the evolution of the MAR features with $B_{\perp }$. (b) $dV/dI$ versus $B_{\perp }$ and bias current $I$, used to estimate the perpendicular critical magnetic field. The complex dependence of the switching current is due to the combination of the Fraunhofer effect and the drop of the switching current as the magnetic field is increasing. (c) $V$ versus in-plane magnetic field $B_{\parallel }$ and $I$, used to estimate the in-plane critical field. (d) $V$ versus $B_{\perp }$ and $I$ at small applied magnetic fields, showing a Fraunhofer-like pattern. The negative values of current indicate retrapping current and the positive values of current indicate switching current in (b), (c) and (d).

Figure 4

(a) False-colored SEM image of the two-JoFET asymmetric SQUID with channel lengths of $150\mathrm{nm}$ and $350\mathrm{nm}$. The scale bar is $1\mu \mathrm{m}$. (b) $V_{\text{G1}}=-1.245\mathrm{V}$ and $V_{\text{G2}}=-9\mathrm{V}$ results in equal critical currents, yielding SQUID-like oscillations of the total critical current as a function of $B_{\perp }$. (c) $V_{\text{G1}}=-8\mathrm{V}$ and $V_{\text{G2}}=-1.4\mathrm{V}$ makes the superconducting phase drop mainly over JoFET2, allowing us to associate the oscillations in the critical current with the current-phase relationship of JoFET2. (d) Critical current extracted from (c) (solid points). The blue line shows a fit of the oscillations to the CPR given in Eq. (2), yielding $\tau =0.88\pm 0.05$. The shaded region indicates the error in $\tau$.