Multiple Andreev reflections and Shapiro steps in a Ge-Si nanowire Josephson junction

Joost Ridderbos, Matthias Brauns, Ang Li, Erik P. A. M. Bakkers, Alexander Brinkman, Wilfred G. van der Wiel, and Floris A. Zwanenburg

Phys. Rev. Materials 3, 084803 – Published 14 August 2019

Abstract

We present a Josephson junction based on a Ge-Si core-shell nanowire with transparent superconducting Al contacts, a building block which could be of considerable interest for investigating Majorana bound states, superconducting qubits, and Andreev (spin) qubits. We demonstrate the dc Josephson effect in the form of a finite supercurrent through the junction and establish the ac Josephson effect by showing up to 23 Shapiro steps. We observe multiple Andreev reflections up to the sixth order, indicating that charges can scatter elastically many times inside our junction and that our interfaces between superconductor and semiconductor are transparent and have low disorder.

Received 14 March 2019
Revised 15 July 2019

DOI:https://doi.org/10.1103/PhysRevMaterials.3.084803

Physics Subject Headings (PhySH)

Andreev reflection Ballistic transport Josephson effect Proximity effect Superconducting gap Superconductors Topological quantum computing

Quantum Information, Science & TechnologyCondensed Matter, Materials & Applied Physics

Authors & Affiliations

Joost Ridderbos¹, Matthias Brauns¹, Ang Li², Erik P. A. M. Bakkers^2,3, Alexander Brinkman¹, Wilfred G. van der Wiel¹, and Floris A. Zwanenburg^1,*

¹MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
²Department of Applied Physics, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands
³QuTech and Kavli Institute of Nanoscience, Delft University of Technology, 2600 GA Delft, The Netherlands

^*f.a.zwanenburg@utwente.nl

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Vol. 3, Iss. 8 — August 2019

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Images

Figure 1
dc Josephson effect in a Ge-Si nanowire. (a) False-color SEM image of the device under investigation. A nanowire with a $20 nm$ diameter lies on the ${SiO}_{2}$ covered substrate and is contacted by an Al source and drain. The channel length is $\sim 150 nm$ with a semiconducting island (red arrow) of $\sim 50 nm$ . (b) $V_{SD}$ vs $I_{S}$ for $V_{BG} = - 7.6 V$ and $V_{BG} = - 15 V$ . $I_{S}$ is swept from left to right (solid) and successively from right to left (dashed) denoted by the colored arrows. $I_{SW}$ and $I_{R}$ are indicated for $V_{BG} = - 7.6 V$ . Horizontal black arrows indicate “wiggles” in the curve corresponding to MAR of the $n th$ order.
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Figure 2
Multiple Andreev reflections up to the sixth order. (a) Differential conductance $\partial I_{S} / \partial V_{SD}$ vs $V_{SD}$ and $V_{BG}$ . The black arrows indicate the sweep direction (see Sec. 9b). Horizontal equipotential lines of increased conductance indicated by the green arrows correspond to MAR. Current biased measurement where the $I_{S}$ and $V_{SD}$ axes were inverted (see Methods) before numerical derivation. Only return current was measured (see black arrows) in a highly hysteretic regime [see blue curve in Fig. 1] to reach the low-voltage regime. (b) Single traces of $\partial I_{S} / \partial V_{SD}$ vs $V_{SD}$ for three values of $V_{BG}$ . Green, orange, and blue (traces offset by $200 μ S$ ) taken at $V_{BG} = - 8.3$ , $- 8$ , and $- 7.6 V$ [see Fig. 2, dashed lines]. Vertical gray dashed lines denote expected MAR peak positions calculated by $n = 2 Δ_{Al} / e V_{SD}$ for $n = 1 – 10$ . Inset: MAR peak positions (P.P.) vs inverse MAR order $1 / n$ at $V_{BG} = - 7.6$ (blue trace) for positive bias. The black line is a linear fit through zero. (c) Same data as (b) plotted vs $n$ , only positive $V_{SD}$ is shown. The vertical dashed gray lines show integers of $n$ which can be matched with the MAR peaks up to $n = 6$ .
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Figure 3
Temperature dependence of MAR and $I_{SW}$ . (a) Differential resistance $\partial V_{SD} / \partial I_{S}$ vs $I_{S}$ and $T$ and (b) differential conductance $\partial I_{S} / \partial V_{SD}$ vs $V_{SD}$ and $T$ , both for the same data with $V_{BG} = - 13.35 V$ . $I_{S}$ and $V_{SD}$ are swept from negative to positive bias. In (a) $I_{SW}$ and $I_{R}$ are denoted by the white arrows and the green dashed line is a fit based on the Eilenberger equations [70]. Black dashed curves in (b) are fits to Eq. (1).
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Figure 4
ac Josephson effect, up to 23 Shapiro steps. (a) $V_{SD}$ vs $I_{S}$ for frequencies $f = 1.51$ , 2.80, and $4.40 GHz$ at respective amplitudes $V_{rms} = 0.11$ , 0.13, and $0.13 V$ . $V_{rms}$ values are ac amplitudes applied before filtering. $f = 2.8 GHz$ results in a step height of $Δ V = 5.8 μ V$ (black arrow). (b) Step height $Δ V$ vs microwave frequency $f$ extracted from data (blue boxes). The black line is a plot of $Δ V = h f / 2 e$ . (c) Differential resistance $\partial V_{SD} / \partial I_{S}$ vs $I_{S}$ and microwave rms voltage $V_{rms}$ applied at a frequency of $2.65 GHz$ at $V_{BG} = - 15 V$ [red curve in Fig. 1]. (d) Left: $\partial I_{S} / \partial V_{SD}$ vs $V_{SD}$ and $V_{rms}$ , same measurement data as (c) with $I_{S}$ and $V_{SD}$ axes reversed before numerical derivation (see Methods). $V_{SD}$ shown in units of $h f / 2 e$ . Right: line cut at $V_{rms} = 0.66 V$ showing 23 peaks.
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Figure 5
Shapiro steps vs backgate voltage. (a) Differential resistance $\partial V_{SD} / \partial I_{S}$ vs $I_{S}$ and $V_{BG}$ at fixed microwave frequency $f = 2.65 GHz$ and $V_{rms} = 0.1 V$ . The direction in which $I_{S}$ is swept is reversed after each step of $V_{BG,step} = 25$ mV. The white dashed line denotes $V_{BG} = - 15 V$ used in Fig. 4. (b) Differential conductance $\partial I_{S} / \partial V_{SD}$ vs $V_{SD}$ (units of $h f / 2 e$ ) vs $V_{BG}$ . Same data set as (a) where $I_{S}$ and $V_{SD}$ axes were inverted (see section Methods). We identify up to five Shapiro steps, i. e., current plateaus $s = 0 – 5$ . The “wavy” pattern, i. e., the gradual shift of the lines in $V_{SD}$ as a function of $V_{BG}$ , is caused by small variations in the leakage current at different $V_{BG}$ .
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