Superconducting Electron Transport in Graphene-Based Josephson Junctions
Graphene – a single atomic layer of graphite – is one of the most studied quasi two-dimensional materials (2D). Its electronic properties are particularly interesting, for example allowing one to study the physics of 2D relativistic electrons. Recently, graphene samples were coupled to superconducting leads, thus forming S-N-S (superconducting-normal-superconducting), or “Josephson” junctions. It was found that superconducting current (“supercurrent”) could flow through the normal (i.e. non-superconducting) graphene regions. The mechanism of this supercurrent is not fully explored. In this work, we study the supercurrent transport in three different regimes dependent on the electronic properties of graphene: diffusive, ballistic and quantum Hall (QH). In a diffusive device, the mean free path (scattering length) ξ_S of an electron is shorter than the length between the SC contacts, L. In the ballistic limit, the scattering length ξ_S exceeds L. These two regimes are explored without external magnetic field. On the other hand, the QH regime is induced by application of a strong magnetic field perpendicular to the plane of the sample. When the cyclotron radius rC is smaller than the junction length L/2, electron trajectories form closed orbits in the bulk of graphene and skipping orbits at the edge. Below I describe our findings in these regimes in more details.
For the diffusive case, the crucial energy scale is the Thouless energy, ETH = ħD/L^2, where D is diffusive constant. We find that the product of the critical current (maximal current through the device) and its normal resistance, I_CR_N, follows a universal linear dependence of E_TH for more than three orders of magnitude. However, the I_CR_N product is found to be much smaller than the theoretically predicted value of ~10E_TH/e.
To explore the ballistic regime, we worked with graphene encapsulated in hexagonal-Boron Nitride (h-BN), which greatly improves the transport properties of graphene. Here, we study the ballistic Josephson junctions in the short and long junction limits, determined by comparing the length of the junction with the induced superconducting coherence length. For the long junction limit, the temperature dependence of supercurrent is controlled by the energy level spacing as extracted from the Fabry-Perot (FP) oscillations. On the other hand, in the short junction limit, the superconducting gap will be the characteristic energy. Furthermore, we also study the supercurrent distribution in the graphene Josephson junctions by measuring the interference pattern in a small magnetic field. A unique periodicity modification around the Dirac point (DP) is observed.
Lastly, we demonstrate the first observation of supercurrent in the QH regime. Since in high magnetic fields the electron trajectories develop into cyclotron orbits, the bulk of the graphene is gapped by the so-called Landau quantization, and the only transport channels are chiral edge states on the borders of graphene. We study the magnetic interference of the supercurrent and demonstrate that the supercurrent indeed flows along the edges of the graphene region. Using different junction geometries, we examine possible mechanisms for this supercurrent. Our results may pave the way to realizing Majorana fermion or parafermion states predicted to be formed in certain hybrid QH-SC devices.
To conclude, we have explored supercurrent transport in multiple different regimes in the graphene Josephson junctions.
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