# Browsing by Subject "Quantum Hall"

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Item Open Access Investigation of Supercurrent in the Quantum Hall Regime in Graphene Josephson Junctions(Journal of Low Temperature Physics, 2018-06-01) Draelos, A; Wei, MT; Seredinski, A; Ke, C; Watanabe, K; Taniguchi, T; Yamamoto, M; Tarucha, S; Borzenets, I; Amet, F; Finkelstein, G© 2018, Springer Science+Business Media, LLC, part of Springer Nature. In this study, we examine multiple encapsulated graphene Josephson junctions to determine which mechanisms may be responsible for the supercurrent observed in the quantum Hall (QH) regime. Rectangular junctions with various widths and lengths were studied to identify which parameters affect the occurrence of QH supercurrent. We also studied additional samples where the graphene region is extended beyond the contacts on one side, making that edge of the mesa significantly longer than the opposite edge. This is done in order to distinguish two potential mechanisms: (a) supercurrents independently flowing along both non-contacted edges of graphene mesa, and (b) opposite sides of the mesa being coupled by hybrid electron–hole modes flowing along the superconductor/graphene boundary. The supercurrent appears suppressed in extended junctions, suggesting the latter mechanism.Item Open Access Superconducting Electron Transport in Graphene-Based Josephson Junctions(2017) Ke, ChungTingGraphene – 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.

Item Open Access Thermal and Electronic Transport in Graphene Superconducting Devices(2018) Draelos, Anne WatsonThis dissertation presents the experimental methods and results of investigations into the nature of thermal and electronic transport at low temperatures in graphene superconducting devices. By coupling graphene to superconductors, we study the nature of complex supercurrent flow in graphene Josephson junctions. Small variations in magnetic fields are used to obtain information about the supercurrent distribution in rectangular two-terminal junctions, and anomalous interference patterns are observed in graphene close to the Dirac point. Extending the number of terminals to a four-terminal device allowed us to study the interplay of various supercurrents in the shared graphene region. Each of the observed supercurrents are identified as specific paths between pairs of terminals and are tracked as a function of charge density in the graphene. Multiple superconducting graphene devices are further studied under high magnetic fields to elucidate the potential transport mechanisms of supercurrent carried by quantum Hall edge states. Finally, we use large-domain graphene to fabricate devices across large length scales in order to study the interdependent heat transfer between electrons and phonons and diffusive electronic processes. With the ability to measure electronic temperature through Universal Conductance Fluctuations we study the heat flow directly as a function of length. Non-uniform thermal gradients are observed and related to equations describing the total heat flux in the graphene device.

Item Open Access Transport Mechanisms of Quantum Hall Supercurrents in Graphene Josephson Junctions(2018) Wei, Ming-TsoThe existence of supercurrent in the quantum Hall regime with periodic magnetic interference patterns, first observed by Amet et al. in 2016, has created new opportunities to access topological superconductivity through quantum Hall edge states. However, a puzzle is found in the measured h/2e periodicity, as it violates the theoretical predicted h/e periodicity of the supercurrents carried by chiral quantum Hall edge states. Thus the observed supercurrents have not yet been robustly confirmed.

In this dissertation, we study the transport mechanisms of supercurrents in the quantum Hall regime in graphene Josephson junctions. First, a device with individually gated vacuum edges extended beyond the contacts is studied to determine whether the measured supercurrents are consistent with the theoretical prediction that both edges participate in transport. Next, a device with a third normal contact on one vacuum edge is used to study how supercurrents are influenced by an injected normal current. Finally, a device with a T-shaped asymmetric contact and a flat contact separated by a 90nm short channel is fabricated to examine the coupling of the chiral electron-hole hybrid modes. Despite that fact that theoretical explanation of the h/2e periodicity are still outstanding, these studies have extended our understanding of supercurrents in the quantum Hall regime. This may lay the foundation of realizing Majorana fermions and parafermions with symmetry-breaking edge states in quantum Hall/superconductor hybrid devices.