The rise of graphene

TL;DR

Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena can now be mimicked and tested in table-top experiments.

Abstract

Graphene is a rapidly rising star on the horizon of materials science and condensed matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed matter physics, where quantum relativistic phenomena, some of which are unobservable in high energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

Figures (6)

• Figure 1: Mother of all graphitic forms. Graphene is a 2D building material for carbon materials of all other dimensionalities. It can be wrapped up into 0D buckyballs, rolled into 1D nanotubes or stacked into 3D graphite.
• Figure 2: One-atom-thick single crystals: the thinnest material you will ever see. a, Graphene visualized by atomic-force microscopy (adapted from ref. 8). The folded region exhibiting a relative height of$\approx 4 \mathring{\mathrm{A}}$ clearly indicates that it is a single layer. b, A graphene sheet freely suspended on a micron-size metallic scaffold. The transmission-electron-microscopy image is adapted from ref. 18. c, scanning-electron micrograph of a relatively large graphene crystal, which shows that most of the crystal's faces are zigzag and armchair edges as indicated by blue and red lines and illustrated in the inset (T.J. Booth, K.S.N, P. Blake & A.K.G. unpublished). 1D transport along zigzag edges and edge-related magnetism are expected to attract significant attention.
• Figure 3: Ballistic electron transport in graphene. a, Ambipolar electric field effect in single-layer graphene. The insets show its conical low-energy spectrum$E(k)$, indicating changes in the position of the Fermi energy $E_{\mathrm{F}}$ with changing gate voltage $V_{\mathrm{g}}$. Positive (negative) $V_{\mathrm{g}}$ induce electrons (holes) in concentrations $n=\alpha V_{\mathrm{g}}$ where the coefficient $\alpha \approx 7.2 \cdot 10^{10} \mathrm{~cm}^{-2} / \mathrm{V}$ for field-effect devices with a 300 nm SiO 2 layer used as a dielectric ${ }^{7-9}$. The rapid decrease in resistivity $\rho$ with adding charge carriers indicates their high mobility (in this case, $\mu \approx 5,000 \mathrm{~cm}^{2} / \mathrm{Vs}$ and does not noticeably change with temperature up to 300K). b, Room-temperature quantum Hall effect (K.S.N., Z. Jiang, Y. Zhang, S.V. Morozov, H.L. Stormer, U. Zeitler, J.C. Maan, G.S. Boebinger, P. Kim & A.K.G. Science 2007, in the press). Because quasiparticles in graphene are massless and also exhibit little scattering even under ambient conditions, the QHE survives up to room $T$. Shown in red is the Hall conductivity $\sigma_{\mathrm{xy}}$ that exhibits clear plateaux at $2 e^{2} / h$ for both electrons and holes. The longitudinal conductivity $\rho_{\mathrm{xx}}$ (blue) reaches zero at the same gate voltages. The inset illustrates the quantized spectrum of graphene where the largest cyclotron gap is described by $\delta E(\mathrm{~K}) \approx 420 \cdot \sqrt{B}(\mathrm{~T})$.
• Figure 4: Chiral quantum Hall effects. a, The hallmark of massless Dirac fermions is QHE plateaux in$\sigma_{\mathrm{xy}}$ at half integers of $4 e^{2} / h$ (adapted from ref. 9). $\mathbf{b}$, Anomalous QHE for massive Dirac fermions in bilayer graphene is more subtle (red curve ${ }^{55}$ ): $\sigma_{\mathrm{xy}}$ exhibits the standard QHE sequence with plateaux at all integer $N$ of $4 e^{2} / h$ except for $N=0$. The missing plateau is indicated by the red arrow. The zero- $N$ plateau can be recovered after chemical doping, which shifts the neutrality point to high $V_{\mathrm{g}}$ so that an asymmetry gap ( $\approx 0.1 \mathrm{eV}$ in this case) is opened by the electric field effect (green curve; adapted from ref. 59). c-e, Different types of Landau quantization in graphene. The sequence of Landau levels in the density of states $D$ is described by $E_{N} \propto \sqrt{N}$ for massless Dirac fermions in single-layer graphene (c) and by $E_{N} \propto \sqrt{N(N-1)}$ for massive Dirac fermions in bilayer graphene (d). The standard LL sequence $E_{N} \propto(N+1 / 2)$ is expected to recover if an electronic gap is opened in the bilayer (e).
• Figure 5: Minimum conductivity of graphene. Independent of their carrier mobility$\mu$, different graphene devices exhibited approximately the same conductivity at the neutrality point (open circles) with most data clustering around $\approx 4 e^{2} / h$ indicated for clarity by the dashed line (A.K.G. & K.S.N. unpublished; includes the published data points from ref. 9). The high-conductivity tail is attributed to macroscopic inhomogeneity: by improving samples’ homogeneity, $\sigma_{\text{min }}$ generally decreases, moving closer to $\approx 4 e^{2} / h$. The green arrow and symbols show one of the devices that initially exhibited an anomalously large value of $\sigma_{\text{min }}$ but after thermal annealing at 400 K its $\sigma_{\text{min }}$ moved closer to the rest of the statistical ensemble. Most of the data are taken in the bend resistance geometry where the macroscopic inhomogeneity plays the least role.