Graphene: Status and Prospects

TL;DR

This review analyzes recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

Abstract

Graphene is a wonder material with many superlatives to its name. It is the thinnest material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have the smallest effective mass (it is zero) and can travel micrometer-long distances without scattering at room temperature. Graphene can sustain current densities 6 orders higher than copper, shows record thermal conductivity and stiffness, is impermeable to gases and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation, which allows the investigation of relativistic quantum phenomena in a bench-top experiment. What are other surprises that graphene keeps in store for us? This review analyses recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.

Figures (4)

• Figure 1: Making graphene. (A) Large graphene crystal prepared on an oxidized Si wafer by the scotch tape technique (courtesy of Graphene Industries Ltd). (B) Suspension of microcrystals obtained by ultrasound cleavage of graphite in chloroform (left). Such suspensions can be printed on various substrates. The resulting films are robust and remain highly conductive even if folded (right; courtesy of R. Nair, Manchester). (C) First graphene wafers. Polycrystalline one-to-five-layer films grown on Ni and transferred onto a Si wafer (courtesy of A. Reina and J. Kong, MIT). (D) State-of-the-art SiC wafer with atomic terraces covered by a graphitic monolayer (indicated by '1'). Double and triple layers (' 2 ' and ' 3 ') grow at the steps (12).
• Figure 2: Quasiparticle zoo. (A) Charge carriers in condensed matter physics are normally described by the Schrödinger equation with an effective mass$m^{*}$ different from the free electron mass ( $p$ is the momentum operator). (B) Relativistic particles in the limit of zero rest mass follow the Dirac equation, where $c$ is the speed of light and $\sigma$ is the Pauli matrix. (C) Charge carriers in graphene are called massless Dirac fermions and described by a 2D analogue of the Dirac equation with the Fermi velocity $v_{\mathrm{F}} \approx 1 \times 10^{6} \mathrm{~m} / \mathrm{s}$ playing the role of the speed of light and a 2D pseudospin matrix $\sigma$ describing two sublattices of the honeycomb lattice (3). Similar to the real spin that can change its direction between, say, left and right, the pseudospin is an index that indicates on which of the two sublattices a quasiparticle is located. The pseudospin can be indicated by color (say, red and green). (D) Bilayer graphene provides us with yet another type of quasiparticles that have no analogies. They are massive Dirac fermions described by a rather bizarre Hamiltonian that combines features of both Dirac and Schrödinger equations. The pseudospin changes its color index 4 times as it moves between four carbon sublattices (2-4).
• Figure 3: Graphene derivatives. (A) Graphene-oxide laminate is tough, flexible, transparent and insulating (6). (B) Paper made in the same way as A but starting from graphene suspension (5) is porous, fragile, opaque and metallic (courtesy of R. Nair, Manchester).
• Figure 4: From dreams to reality. (A) Graphene nanoribbons of sub-10-nm scale exhibit the transistor action with large on-off ratios (22,25). Scanning electron micrograph shows such a ribbon made by electron-beam lithography (22). Control of ribbon's width and its edge structure with atomic precision remains a daunting challenge on the way towards graphene-based electronics. (B) All the fundamentals are in place to make graphene-based HEMTs. The false colour micrograph shows the source and drain contacts in yellow, two top gates in light grey and graphene underneath in green (38). Courtesy of Y. Lin, IBM. (C) Graphene-based NEMS. Shown is a drum resonator made from a$10-\mathrm{nm}-$ thick film of reduced graphene oxide, which covers a recess in a Si wafer (32). (D) Ready to use: graphene membranes provide an ideal support for TEM. The central part is a monolayer of amorphous carbon. Graphene itself shows in this image only as a grey background (see the top part). Carbon atoms in the amorphous layer appear dark and make a random array of pentagons, hexagons and heptagons as indicated by colour lines (courtesy of J. C. Meyer, A. Chuvilin and U. Kaiser, Ulm). Individual oxygen atoms clearly visible on graphene were also reported (36).