Session Q29: Focus Session: Carbon Nanotubes and Related Materials X: p-n Junctions and Mesoscopic Effects in Graphene

Local-Gating of Graphene Nanostructures

We report on the fabrication and measurement of locally-gated single-layer graphene devices. Utilizing a non-covalent functionalization layer, the preservation of the unique electrical properties of graphene after deposition of the top-gate oxide is demonstrated. Novel top-gate geometries, including circular and multiple-rectangular gate designs, combined with oxygen-plasma etching allow for further elucidation of the unique transport properties of graphene p-n junctions and graphene constrictions. Research supported in part by INDEX, an NRI Center, and by the Harvard NSEC.   

Scanning tunneling microscopy and spectroscopy of graphene.

We report low temperature high magnetic field scanning tunneling microscopy and spectroscopy on a graphene sheet suspended above a graphite substrate by extended defects. The measurements provide the first observation of the V-shaped density of states in zero field and of the Landau level (LL) spectrum in finite fields. The LL spectrum consists of a single sequence exhibiting square root dependence on field and level-index, and contains a zero energy LL attesting to the chiral nature of the Dirac Fermion quasiparticles. The density of states reflects important effects due to electron-phonon interactions and to confinement. These include a reduced Fermi velocity, a small (10 meV) gap at the Dirac point, splitting of the n=0 LL at relatively low fields and a new negative energy state that emerges from the Fermi level and splits away linearly with increasing field.   

Electronic properties of one-dimensional graphene bilayer ribbons

The electronic properties of armchair and zigzag bilayer graphene nanoribbons are studied using \textit{ab-initio} density functional theory. We study the effect of width and the electric fields (upto the dielectric breakdown field of SiO2) on their energy gaps [Sahu 2007]. We find metallic and semiconductor arm-chair ribbons and electric field has the effect of increasing the gap in metallic ribbons. The zigzag ribbons due to the edge magnetism show opposite behavior: gap decreases with increase in the applied electric field. We studied small ribbons (below 1 nm) as well as large ribbons (5 nm). In small width arm-chair semiconductor ribbons, the gap decreases whereas in the large width ribbons, the gap increases with applied electric field. Sahu B, Min H, MacDonald AH, and Banerjee SK ``Electronic properties of one-dimensional graphene bilayer ribbons'' (Submitted to Physical Review B).   

Strong Coulomb interactions and weak disorder in graphene

We analyze the instabilities and compute the transport properties of the low-temperature conducting phase of graphene, using a model that incorporates both Coulomb electron-electron interaction and weak quenched disorder effects. Strong Coulomb interactions are treated within the large-N expansion. Using a perturbative renormalization group (RG) approach to study the effects of virtual processes, we find that at successively lower energy scales, for moderate to strong Coulomb interaction strengths, a type of non-Abelian vector potential disorder always asserts itself as the dominant \emph{elastic} scattering mechanism for generic short-ranged microscopic defect distributions. Vector potential disorder appears in graphene due to, e.g., elastic lattice deformations (``ripples''). We combine the RG results with a quantum kinetic equation analysis of real processes, i.e.\ inelastic electron-electron scattering, which allows us to compute the temperature- and chemical potential-dependence of electric and thermal transport coefficients due to elastic and inelastic scattering processes in various coupling regimes.   

Electric Field Effect in Epitaxial Graphene Devices

The electric field effect has been observed on epitaxial graphene multilayers grown on SiC substrates by thermal decomposition of SiC. Carriers mobilities up to 2.5$\times $10$^{4}$cm$^{2}$/Vs have been measured. Both side-gated and top-gated graphene field effect transistors (FETs) have been fabricated using standard semiconductor processes on both the Si and the C face of the SiC substrates. In side-gated FETs, the gates are located on both sides of narrow graphene ribbons; source-drain resistances decrease by several percent with a gate bias of several volts. For top-gated FETs the resistance swing reaches a factor of 25. At the gate voltage corresponding to the maximum source-drain resistance, the Hall voltage changes sign indicating a transition from hole- to electron- carried transport, consistent with the graphene band structure. These results indicate the potential of epitaxial graphene as a platform for large-scale graphene based electronics.   

Free-Standing 2-D Graphene Carbon Nanostructures

Carbon nanosheets -- a new, free-standing, two-dimensional carbon nanostructure -- have been deposited on a metal, semiconductor, and insulating substrates by RF PECVD. Raman, SEM, TEM, SAED, XPS, AES, FTIR, and XRD all indicate that nanosheets are graphite sheets up to 8 $\mu $m in height but $\le $1 nm in edge thickness. The nanosheets stand off the growth substrate in a manner similar to aligned nanotubes grown by CVD. In contrast to nanotubes, nanosheets do not require catalyst for growth and can be patterned after deposition using standard lithographic techniques. Hydrogen etching promotes the formation of the atomically thin structures while the anisotropic dipole created in the graphene planes by the plasma sheath promotes the vertical orientation. Due to their uniform height and the large number of edge emission sites, nanosheets have proven to be excellent field emitters. Nanosheet samples have produced up to 33 mA of current (32 mm$^{2}$ sample area); similar nanosheet samples have sustained 1.3 mA of current over 200 hours of testing with no degradation.   

Superconducting Proximity Effect in Graphite Films

Theoretical analysis of superconducting current in graphite films (or graphen)in proximity to superconductors is presented. In this work, the band structure of the graphite film is treated seriously: because of the delicate band structure of graphite, the actual band structure of the film, which undergoes the effects of various external factors such as leads and gates, can show a wide variety. We introduce following three models: 1) graphen-like Fermi points, 2) semi-metal, 3) electron (or hole) pockets, and 4) semiconducting gap. The superconducting critical current I{\_}c = exp {\{}- L/xi(T){\}} is studied where L is the distance between two leads and xi(T) is the coherence length in the graphite film. The temperature dependence of xi(T) is largely affected by the band structure and by examining this dependence the electronic properties of the graphite film can be estimated. The results are compared with actual experiments.   

Superconducting proximity effect in thin graphite films

Gate-controlled superconducting proximity effect in thin graphite films is reported. A graphite film with thickness of 4 - 10 nm is connected to two aluminum superconducting electrodes, forming a SNS junction, and gate electric field is applied using a back gate. The critical supercurrent displays an ambipolar behavior, and for a fixed normal-state resistance the electron critical supercurrent with positive gate voltage is always larger than the hole critical supercurrent with negative gate voltage (electron-hole symmetry breaking). This effect is also observed in the critical temperature where the junction resistance vanishes. Furthermore, the critical supercurrent is proportional to $\exp(-(T/T_0)^2)$, which has never been observed in other SNS systems. The details of the experimental results as well as their possible origins will be discussed.   

Supercurrent in Graphene Josephson Transistors

We investigate electrical transport in single or bi-layer graphene devices coupled to superconducting electrodes. In these two-dimensional Josephson junctions, we observed gate tunable supercurrent, multiple Andreev reflections and hysteretic current-voltage characteristics. Latest experimental progress on dependence of supercurrent on temperature, number of layers and source-drain separation will be discussed.   

Conductance behaviors of point-contact graphite junctions with normal metal and superconducting tips

The recent discovery of graphene, a truly two-dimensional carbon allotrope, has attracted great interest because of its novel physics and potential for new electronic device applications. Among a variety of theoretical predictions that await stringent experimental tests, reflectionless tunneling (Klein paradox) and specular Andreev reflection are most intriguing. Aiming at eventually probing such unique charge transport phenomena in graphene junctions, we first investigate conductance behaviors of the nanoscale graphite junctions made by point-contact techniques using simple metal (Au) and superconducting (Nb) tips. At low temperatures, the conductance data exhibit an inverse peak structure centered at zero bias, reminiscent of the theoretical density of states arising from the Dirac-like dispersion relation. Junctions with Nb show the additional superconducting gap feature. We will present sets of conductance spectra as a function of temperature, magnetic field, and gate voltage, and discuss possible mechanisms to explain the observed conductance behaviors.   

Josephson Current and Multiple Andreev Reflections in Graphene SNS Junctions

The Josephson Effect and Superconducting Proximity Effect were observed in Superconductor-Graphene-Superconductor (SGS) Josephson junctions with coherence lengths comparable to the distance between the superconducting leads. By comparing the measured temperature and gate dependence of the supercurrent and the proximity induced sub-gap features (multiple Andreev reflections) to theoretical predictions, we find that the diffusive junction model yields close quantitative agreement with the results. This is consistent with the fact that the measured mean free paths in these junctions, 10 $\sim $ 30 nm, are significantly shorter than the lead separation. We show that all SGS devices reported so far fall in the diffusive junction category.   

Electric field effect modulation and hysteresis in thin graphite using ferroelectric gate oxides

We study the electronic properties of thin graphite field effect transistors (FETs) using ferroelectric gate oxide Pb (Zr,Ti)O$_3$ (PZT). Thin graphite flakes (3-5nm) are exfoliated onto 300 nm PZT films epitaxially grown on doped SrTiO$_3$ (STO) and fabricated into FET devices. Carriers are induced into the FETs by applying a voltage V$_g$ on the STO substrate (backgate). We observe a maximum carrier density ($n$) of $\sim$4x10$^{13}$cm$^{-2}$ and a density modulation of $\sim$2x$^{12}$cm$^{-2}$/V$_g$(V), and extract a high dielectric constant $\sim$100 of PZT. We also explore the potential of non-volatile memory devices based on the large polarization of PZT ($\sim$40 $\mu$C/cm$^2$) and its field switching behavior. At 300 K, both the resistance and $n$ of the devices show pronounced hysteretic behavior as V$_g$ is swept beyond 3 V, with two distinct states. The unstable one decays exponentially with time, with a time constant of $\sim$6 hours at 300 K and a few days at 150 K, suggesting a thermally activated process. We discuss possible origins of the hysteresis, highlighting the importance of adsorbates at the interface of PZT and graphite.