We experimentally investigate electrical transport properties of graphene, which is a two dimensional (2D) conductor with relativistic energy dispersion relation. By investigating single-and bi-layer graphene devices with different aspect ratios, we confirm experimentally that the minimum conductivity in wide and short graphene strips approaches the universal value of 4e 2 /πh. At low temperatures, quantum interference of multiply-reflected waves of electrons and holes in graphene give rise to periodic conductance oscillations with bias and gate voltages. Thus graphene acts as a quantum billiard, a 2D ballistic, phase coherent electron system with long phase coherence length that exceeds 5 µm. Additional features in differential conductance emerge when graphene is coupled to superconducting electrodes. We observe proximity-induced enhanced conductance at low bias, and conductance dips at energy scales far above the superconducting gap of the electrodes. The latter provides preliminary evidence for a novel superconducting material that consists of graphene coated with metallic atoms. *To whom correspondence should be addressed. Email: lau@physics.ucr.edu Graphene, a two-dimensional (2D) a honey-comb lattice of carbon atoms, exhibits rather unusual energy dispersion relations -the low-lying electrons in single layer graphene behave like massless relativistic Dirac fermions with vanishing density of states at the Dirac point, and bilayer's band structure resembles that of a zero band gap semiconductor (Fig. 1a). Since recent experimental isolation and measurement of graphene [1][2][3], it has attracted tremendous attention, as the special band structures in single and bi-layer graphenes yield novel aspects to the physics of two-dimensional electron systems. The Dirac spectrum in graphene is predicted to give rise to a number of phenomena, such as quantum spin hall effects [4][5][6], enhanced Coulomb interaction [7][8][9][10][11], and suppression of weak localization [12,13]. Technologically, graphene is an attractive material for nanoscale electronics engineering. As a two-dimensional (2D) relative of carbon nanotubes, it manifests high mobility, extraordinary thermal conductivity and atomic perfection; but in contrast to nanotubes, traditional lithographic techniques can potentially be employed for tailoring of transport properties and device synthesis [14].In the past two years, much progress has been made on theoretical understanding of the novel electronic properties that may emerge in graphene. In contrast, experimental measurements of graphene have been relatively scarce.Here we demonstrate experimentally that single layer (SLG) and bi-layer (BLG) graphene can act as a quantum billiard, i.e. a 2D ballistic system where scattering only occur at boundaries, with a phase coherence length that exceeds 5 µm. The ballistic transport for charge carriers, coupled with phase coherent multiple-reflection at the electrodes, give rise to quantum interference of waves of the charge carriers, thus realizing a quant...

We report experiments on quantum dot single-electron-tunneling (SET) transistors made from short multiwall nanotubes and threaded by magnetic flux. Such systems allow us to probe the electronic energy spectrum of the nanotube and its dependence on the magnetic field. Evidence is provided for the interconversion between gapped (semiconducting) and ungapped (metallic) states. Our tubes exhibit h/e-period magnetic flux dependence, in agreement with simple tight-binding calculations.

We study the stochastic nature of switching current in hysteretic current-voltage characteristics of superconductor-graphene-superconductor junctions. We find that the dispersion of the switching current distribution scales with temperature as σ(I) proportional to T(α(G)) with α(G) as low as 1/3. This observation is in sharp contrast to the known Josephson junction behavior where σ(I) proportional to T(α(J)) with α(J)=2/3. We propose an explanation using a generalized version of Kurkijärvi's theory for the flux stability in rf-SQUID and attribute this anomalous effect to the temperature dependence of the critical current which persists down to low temperatures.

We examine the nature of the transitions between the normal and superconducting branches in superconductor-graphene-superconductor Josephson junctions. We attribute the hysteresis between the switching (superconducting to normal) and retrapping (normal to superconducting) transitions to electron overheating. In particular, we demonstrate that the retrapping current corresponds to the critical current at an elevated temperature, where the heating is caused by the retrapping current itself. The superconducting gap in the leads suppresses the hot electron outflow, allowing us to further study electron thermalization by phonons at low temperatures (T≲1 K). The relationship between the applied power and the electron temperature was found to be P∝T3, which we argue is consistent with cooling due to electron-phonon interactions.

We report on graphene-based Josephson junctions with contacts made from lead. The high transition temperature of this superconductor allows us to observe the supercurrent branch at temperatures up to ∼ 2 K, at which point we can detect a small, but non-zero, resistance. We attribute this resistance to the phase diffusion mechanism, which has not been yet identified in graphene. By measuring the resistance as a function of temperature and gate voltage, we can further characterize the nature of electromagnetic environment and dissipation in our samples. PACS numbers: 74.45.+c, 74.50.+r, 72.80.Vp Josephson junctions with a normal metal region sandwiched between two superconductors are known as superconductor-normal-superconductor (SNS) structures. Over the years, the normal region has been made from non-metallic nanostructures, including heterostructures, nanotubes, quantum wires, quantum dots [1], and, most recently, graphene [2][3][4][5]. Usually, these superconductor-graphene-superconductor (SGS) junctions employ aluminum as the superconducting metal, separated from graphene by another metal layer (often titanium) intended to create a good contact. In this paper, we succeed in making palladium-lead (Pd/Pb) contacts to graphene. Here, Pd is known to form low-resistance contacts to graphene [6,7], while Pb has the advantage of a relatively large critical temperature (7.2 K). As a result, the SGS junctions demonstrate an enhanced zerobias conductance up to temperatures of the order of 5 K, and at temperatures below ∼ 2 K a clearly visible supercurrent branch appears in the I − V curves.In all of our samples, a small, but non-zero voltage is observed below the switching current. We attribute this feature to the phase diffusion mechanism [8]. The phase diffusion in underdamped junctions is enabled by the junction's environment, which provides dissipation at high frequencies [9]. Observation of this regime in our SGS junctions is facilitated by the high critical temperature of Pb. We first study the phase diffusion resistance as a function of temperature, which allows us to extract the activation energy associated with the phase slips. Next, the phase diffusion is measured at different gate voltages, resulting in a consistent picture of the junction's environment and dissipation at high frequencies. This series of measurements allows us both to establish the phase diffusion regime in underdamped SGS junctions, and to analyze their behavior in terms of well-established models. Finally, we demonstrate an efficient way of controlling the junction by passing a current through one of the electrodes within the same structure: the locally created magnetic field modulates the critical current. Several periods of oscillations are visible, indicating the spatial uniformity of the junction.Graphene was prepared by a version of the conventional exfoliation recipe [10] from natural graphite stamped on RCA-cleaned Si/SiO 2 substrates. The samples were verified by Raman spectroscopy to be single atomic layer thick with low defect...