Tuning the supercurrent distribution in parallel ballistic graphene Josephson junctions

Philipp Schmidt, Luca Banszerus, Benedikt Frohn, Stefan Blien, Kenji Watanabe, Takashi Taniguchi, Andreas K. Hüttel, Bernd Beschoten, Fabian Hassler, and Christoph Stampfer

Phys. Rev. Applied 20, 054049 – Published 22 November 2023

Abstract

We report on a ballistic and fully tunable Josephson-junction system consisting of two parallel ribbons of graphene in contact with superconducting molybdenum-rhenium. By electrostatic gating of the two individual graphene ribbons, we gain control over the real-space distribution of the superconducting current density, which can be continuously tuned between the two ribbons. We extract the respective gate-dependent spatial distributions of the real-space current density by employing Fourier and Hilbert transformations of the magnetic-field-induced modulation of the critical current. This approach is fast and does not rely on a symmetric current profile. It is therefore a universally applicable tool, potentially useful for carefully adjusting Josephson junctions.

Received 11 February 2023
Revised 30 August 2023
Accepted 2 November 2023

DOI:https://doi.org/10.1103/PhysRevApplied.20.054049

Physics Subject Headings (PhySH)

Ballistic transport Critical current

Graphene Josephson junctions Nanoribbon

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Philipp Schmidt ^1,2,*, Luca Banszerus ^1,2, Benedikt Frohn¹, Stefan Blien ³, Kenji Watanabe ⁴, Takashi Taniguchi ⁵, Andreas K. Hüttel ³, Bernd Beschoten ¹, Fabian Hassler ⁶, and Christoph Stampfer ^1,2

¹JARA-FIT and 2nd Institute of Physics, RWTH Aachen University, Aachen 52074, Germany
²Peter Grünberg Institute (PGI-9), Forschungszentrum Jülich, Jülich 52425, Germany
³Institute for Experimental and Applied Physics, University of Regensburg, Regensburg 93040, Germany
⁴Research Center for Functional Materials, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁵International Center for Materials Nanoarchitectonics, National Institute for Materials Science, 1-1 Namiki, Tsukuba 305-0044, Japan
⁶JARA-Institute for Quantum Information, RWTH Aachen University, Aachen 52056, Germany

^*philipp.schmidt3@rwth-aachen.de

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Vol. 20, Iss. 5 — November 2023

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Images

Figure 1
(a) Schematic of the device structure and optical micrograph of the device. Two etched graphene ribbons (1 and 2) encapsulated in $h$ -BN are contacted with superconducting Mo-Re. In addition to the global ${Si}^{+ +}$ back gate, a Cr/Au top gate is deposited onto one of the ribbons (not shown in the micrograph), separated by a layer of aluminum oxide ( ${Al}_{2} O_{3}$ ). A constant bias voltage $V_{bias}$ is applied and the resulting current $I$ is measured. (b) Schematic of the doping configurations accessible with the two gates. The Mo-Re contacts induce a persistent $\tilde{n}$ doping at their graphene interfaces. (c) Differential conductance as a function of charge carrier density $n_{2}$ in the top-gated graphene ribbon and current ( $T \approx 10 mK$ ). The superconducting regime around $I = 0$ is well visible. For $p$ doping, i.e., $n < 0$ , Fabry-Perot oscillations (see vertical arrows) are visible in the critical current. (d) Normal state conductance as a function of top-gate voltage $V_{TG}$ with reference to the charge neutrality point. The Fabry-Perot oscillations are also marked by arrows. The inset shows a sketch of the device with the relevant dimensions. (e) The normal state conductance versus applied top- and back-gate voltages showing four electrostatic doping regimes of the graphene ribbons. The white vertical line corresponds to the position of the line trace shown in panel (d). (f) The gate-dependent critical currents show a tuning similar to the normal state conductance in panel (e).
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Figure 2
(a) Differential conductance as a function of current and out-of-plane magnetic field for the gating configuration of one conductive, $n$ -doped graphene ribbon while the other is tuned to charge neutrality [see inset of panel (b)]. The critical current shows a Fraunhofer-like modulation pattern. (b) The extracted real-space current density confirms the expected asymmetric current distribution by the pronounced peak at $y > 0$ . (c) Differential conductance map for the case where both ribbons are $p$ -doped. The magnetic-field-induced modulation of the critical current changes to a more superconducting-quantum-interference-device-like behavior. (d) The resulting real-space current density shows two peaks with almost equal intensities, proving the symmetric current distribution in the two ribbons.
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Figure 3
(a) Modulation of the critical current (in logarithmic scale) as a function of out-of-plane magnetic field and back-gate voltage at fixed $V_{TG} = 6.3 V$ . The modulation pattern changes with applied gate voltage. (b) Line-wise reconstruction from the data in panel (a) resulting in the real-space position and gate-voltage-dependent superconducting current density distribution. The current density shows a nonsymmetric distribution as well as a symmetrical influence of the back gate on the two graphene ribbons.
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Figure 4
(a) Superconducting current density as a function of real-space position and back-gate voltage for a doping configuration where both ribbons are tuned by the back gate with fixed top-gate voltage. The inset illustrates the respective doping configuration changing from $p | p$ to $n | p$ with increasing gate voltage. (b) Line profile of the superconducting current density along the white dashed line in panel (a). The asymmetric current distribution between the two ribbons can be well identified. The gray areas correspond to the lithographically defined positions of the graphene ribbons 1 and 2. (c) Line profiles of the current densities along the gate axis at the left and right junctions indicated by blue and red triangles in panel (a), respectively. The Fabry-Perot oscillations, marked by the black arrows, can also be seen in the current density. (d)–(f) Similar to (a)–(c) but where the top-gate voltage is varied while both ribbons are $p$ -doped, leading to a symmetric current distribution. (g)–(i) Similar as (d)–(f) but ribbon 1 is tuned to the charge neutrality point. Therefore, almost all the current flows through ribbon 2, leading to a highly asymmetric current distribution.
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