The rise of graphene

PROGRESS ARTICLE nature materials | VOL 6 | MARCH 2007 | www.nature.com/naturematerials 183 A. K. GEIM AND K. S. NOVOSELOV Manchester Centre for Mesoscience and Nanotechnology, University of Manchester, Oxford Road, Manchester M13 9PL, UK *e-mail: geim@man.ac.uk; kostya@graphene.org Graphene is the name given to a fl at monolayer of carbon atoms tightly packed into a two-dimensional (2D) honeycomb lattice, and is a basic building block for graphitic materials of all other dimensionalities (Fig. 1). It can be wrapped up into 0D fullerenes, rolled into 1D nanotubes or stacked into 3D graphite. Th eoretically, graphene (or ‘2D graphite’) has been studied for sixty years1–3, and is widely used for describing properties of various carbon-based materials. Forty years later, it was realized that graphene also provides an excellent condensed-matter analogue of (2+1)-dimensional quantum electrodynamics4–6, which propelled graphene into a thriving theoretical toy model. On the other hand, although known as an integral part of 3D materials, graphene was presumed not to exist in the free state, being described as an ‘academic’ material5 and was believed to be unstable with respect to the formation of curved structures such as soot, fullerenes and nanotubes. Suddenly, the vintage model turned into reality, when free-standing graphene was unexpectedly found three years ago7,8 — and especially when the follow-up experiments9,10 confi rmed that its charge carriers were indeed massless Dirac fermions. So, the graphene ‘gold rush’ has begun. MATERIALS THAT SHOULD NOT EXIST More than 70 years ago, Landau and Peierls argued that strictly 2D crystals were thermodynamically unstable and could not exist11,12. Th eir theory pointed out that a divergent contribution of thermal fl uctuations in low-dimensional crystal lattices should lead to such displacements of atoms that they become comparable to interatomic distances at any fi nite temperature13. Th e argument was later extended by Mermin14 and is strongly supported by an omnibus of experimental observations. Indeed, the melting temperature of thin fi lms rapidly decreases with decreasing thickness, and the fi lms become unstable (segregate into islands or decompose) at a thickness of, typically, dozens of atomic layers15,16. For this reason, atomic monolayers have so far been known only as an integral part of larger 3D structures, usually grown epitaxially on top of monocrystals with matching crystal lattices15,16. Without such a 3D base, 2D materials were presumed not to exist, until 2004, when the common wisdom was fl aunted by the experimental discovery of graphene7 and other free-standing 2D atomic crystals (for example, single-layer boron nitride and half-layer BSCCO)8. Th ese crystals could be obtained on top of non-crystalline substrates8–10, in liquid suspension7,17 and as suspended membranes18. Importantly, the 2D crystals were found not only to be continuous but to exhibit high crystal quality7–10,17,18. Th e latter is most obvious for the case of graphene, in which charge carriers can travel thousands of interatomic distances without scattering7–10. With the benefi t of hindsight, the existence of such one-atom-thick crystals can be reconciled with theory. Indeed, it can be argued that the obtained 2D crystallites are quenched in a metastable state because they are extracted from 3D materials, whereas their small size (<<1 mm) and strong interatomic bonds ensure that thermal fl uctuations cannot lead to the generation of dislocations or other crystal defects even at elevated temperature13,14. A complementary viewpoint is that the extracted 2D crystals become intrinsically stable by gentle crumpling in the third dimension18,19 (for an artist’s impression of the crumpling, see the cover of this issue). Such 3D warping (observed on a lateral scale of ≈10 nm)18 leads to a gain in elastic energy but suppresses thermal vibrations (anomalously large in 2D), which above a certain temperature can minimize the total free energy19. BRIEF HISTORY OF GRAPHENE Before reviewing the earlier work on graphene, it is useful to defi ne what 2D crystals are. Obviously, a single atomic plane is a 2D The rise of graphene 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 briefl y 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. nmat1849 Geim Progress Article.i183 183nmat1849 Geim Progress Article.i183 183 8/2/07 16:22:238/2/07 16:22:23 PROGRESS ARTICLE 184 nature materials | VOL 6 | MARCH 2007 | www.nature.com/naturematerials crystal, whereas 100 layers should be considered as a thin fi lm of a 3D material. But how many layers are needed before the structure is regarded as 3D? For the case of graphene, the situation has recently become reasonably clear. It was shown that the electronic structure rapidly evolves with the number of layers, approaching the 3D limit of graphite at 10 layers20. Moreover, only graphene and, to a good approximation, its bilayer has simple electronic spectra: they are both zero-gap semiconductors (they can also be referred to as zero-overlap semimetals) with one type of electron and one type of hole. For three or more layers, the spectra become increasingly complicated: Several charge carriers appear7,21, and the conduction and valence bands start notably overlapping7,20. Th is allows single-, double- and few- (3 to <10) layer graphene to be distinguished as three diff erent types of 2D crystals (‘graphenes’). Th icker structures should be considered, to all intents and purposes, as thin fi lms of graphite. From the experimental point of view, such a defi nition is also sensible. Th e screening length in graphite is only ≈5 Å (that is, less than two layers in thickness)21 and, hence, one must diff erentiate between the surface and the bulk even for fi lms as thin as fi ve layers21,22. Earlier attempts to isolate graphene concentrated on chemical exfoliation. To this end, bulk graphite was fi rst intercalated23 so that graphene planes became separated by layers of intervening atoms or molecules. Th is usually resulted in new 3D materials23. However, in certain cases, large molecules could be inserted between atomic planes, providing greater separation such that the resulting compounds could be considered as isolated graphene layers embedded in a 3D matrix. Furthermore, one can oft en get rid of intercalating molecules in a chemical reaction to obtain a sludge consisting of restacked and scrolled graphene sheets24–26. Because of its uncontrollable character, graphitic sludge has so far attracted only limited interest. Th ere have also been a small number of attempts to grow graphene. Th e same approach as generally used for the growth of carbon nanotubes so far only produced graphite fi lms thicker than ≈100 layers27. On the other hand, single- and few-layer graphene have been grown epitaxially by chemical vapour deposition of hydrocarbons on metal substrates28,29 and by thermal decomposition of SiC (refs 30–34). Such fi lms were studied by surface science techniques, and their quality and continuity remained unknown. Only lately, few-layer graphene obtained on SiC was characterized with respect to its electronic properties, revealing high-mobility charge carriers32,33. Epitaxial growth of graphene off ers probably the only viable route towards electronic applications and, with so much 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. nmat1849 Geim Progress Article.i184 184nmat1849 Geim Progress Article.i184 184 8/2/07 16:22:278/2/07 16:22:27 PROGRESS ARTICLE nature materials | VOL 6 | MARCH 2007 | www.nature.com/naturematerials 185 at stake, rapid progress in this direction is expected. Th e approach that seems promising but has not been attempted yet is the use of the previously demonstrated epitaxy on catalytic surfaces28,29 (such as Ni or Pt) followed by the deposition of an insulating support on top of graphene and chemical removal of the primary metallic substrate. THE ART OF GRAPHITE DRAWING In the absence of quality graphene wafers, most experimental groups are currently using samples obtained by micromechanical cleavage of bulk graphite, the same technique that allowed the isolation of graphene for the fi rst time7,8. Aft er fi ne-tuning, the technique8 now provides high-quality graphene crystallites up to 100 μm in size, which is suffi cient for most research purposes (see Fig. 2). Superfi cially, the technique looks no more sophisticated than drawing with a piece of graphite8 or its repeated peeling with adhesive tape7 until the thinnest fl akes are found. A similar approach was tried by other groups (earlier35 and somewhat later but independently22,36) but only graphite fl akes 20 to 100 layers thick were found. Th e problem is that graphene crystallites left on a substrate are extremely rare and hidden in a ‘haystack’ of thousands of thick (graphite) fl akes. So, even if one were deliberately searching for graphene by using modern techniques for studying atomically thin materials, it would be impossible to fi nd those several micrometre-size crystallites dispersed over, typically, a 1-cm2 area. For example, scanning-probe microscopy has too low throughput to search for graphene, whereas scanning electron microscopy is unsuitable because of the absence of clear signatures for the number of atomic layers. Th e critical ingredient for success was the observation that graphene becomes visible in an optical microscope if placed on top of a Si wafer with a carefully chosen thickness of SiO2, owing to a feeble interference-like contrast with respect to an empty wafer. If not for this simple yet eff ective way to scan substrates in search of graphene crystallites, they would probably remain undiscovered today. Indeed, even knowing the exact recipe8, it requires special care and perseverance to fi nd graphene. For example, only a 5% diff erence in SiO2 thickness (315 nm instead of the current standard of 300 nm) can make single-layer graphene completely invisible. Careful selection of the initial graphite material (so that it has largest possible grains) and the use of freshly cleaved and cleaned surfaces of graphite and SiO2 can also make all the diff erence. Note that graphene was recently37,38 found to have a clear signature in Raman microscopy, which makes this technique useful for quick inspection of thickness, even though potential crystallites still have to be fi rst hunted for in an optical microscope. Similar stories could be told about other 2D crystals (particularly, dichalcogenide monolayers) where many attempts were made to split these strongly layered materials into individual planes39,40. However, the crucial step of isolating monolayers to assess their properties individually was never achieved. Now, by using the same approach as demonstrated for graphene, it is possible to investigate potentially hundreds of diff erent 2D crystals8 in search of new phenomena and applications. FERMIONS GO BALLISTIC Although there is a whole new class of 2D materials, all experimental and theoretical eff orts have so far focused on graphene, somehow ignoring the existence of other 2D crystals. It remains to be seen whether this bias is justifi ed, but the primary reason for it is clear: the exceptional electronic quality exhibited by the isolated graphene crystallites7–10. From experience, people know that high-quality samples always yield new physics, and this understanding has played a major role in focusing attention on graphene. Graphene’s quality clearly reveals itself in a pronounced ambipolar electric fi eld eff ect (Fig. 3) such that charge carriers can be tuned continuously between electrons and holes in concentrations n as high as 1013 cm–2 and their mobilities μ can exceed 15,000 cm2 V–1 s–1 even under ambient conditions7–10. Moreover, the observed mobilities weakly depend on temperature T, which means that μ at 300 K is still limited by impurity scattering, and therefore can be improved signifi cantly, perhaps, even up to ≈100,000 cm2 V–1 s–1. Although some semiconductors exhibit room- temperature μ as high as ≈77,000 cm2 V–1 s–1 (namely, InSb), those values are quoted for undoped bulk semiconductors. In graphene, μ remains high even at high n (>1012 cm–2) in both electrically and chemically doped devices41, which translates into ballistic transport on the submicrometre scale (currently up to ≈0.3 μm at 300 K). A further indication of the system’s extreme electronic quality is the quantum Hall eff ect (QHE) that can be observed in graphene even at room temperature, extending the previous temperature range for the QHE by a factor of 10 (ref. 42). An equally important reason for the interest in graphene is a particular unique nature of its charge carriers. In condensed- matter physics, the Schrödinger equation rules the world, usually being quite suffi cient to describe electronic properties of materials. Graphene is an exception — its charge carriers mimic relativistic particles and are more easily and naturally described starting with the Dirac equation rather than the Schrödinger equation4–6,43–48. 0 9 Å 13 Å 1 μm 10 μm 1 μm Crystal faces a b c 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 ≈4 Å clearly indicates that it is a single layer. (Copyright National Academy of Sciences, USA.) b, A graphene sheet freely suspended on a micrometre-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 and A.K.G. unpublished work). 1D transport along zigzag edges and edge-related magnetism are expected to attract signifi cant attention. nmat1849 Geim Progress Article.i185 185nmat1849 Geim Progress Article.i185 185 8/2/07 16:22:288/2/07 16:22:28 PROGRESS ARTICLE 186 nature materials | VOL 6 | MARCH 2007 | www.nature.com/naturematerials Although there is nothing particularly relativistic about electrons moving around carbon atoms, their interaction with the periodic potential of graphene’s honeycomb lattice gives rise to new quasiparticles that at low energies E are accurately described by the (2+1)-dimensional Dirac equation with an eff ective speed of light vF ≈ 106 m–1s–1. Th ese quasiparticles, called massless Dirac fermions, can be seen as electrons that have lost their rest mass m0 or as neutrinos that acquired the electron charge e. Th e relativistic- like description of electron waves on honeycomb lattices has been known theoretically for many years, never failing to attract attention, and the experimental discovery of graphene now provides a way to probe quantum electrodynamics (QED) phenomena by measuring graphene’s electronic properties. QED IN A PENCIL TRACE From the point of view of its electronic properties, graphene is a zero-gap semiconductor, in which low-E quasiparticles within each valley can formally be described by the Dirac-like hamiltonian 0 0kx+iky kx–iky = =ћ σ ·kνF ћνFH , (1) where k is the quasiparticle momentum, σ the 2D Pauli matrix and the k-independent Fermi velocity νF plays the role of the speed of light. Th e Dirac equation is a direct consequence of graphene’s crystal symmetry. Its honeycomb lattice is made up of two equivalent carbon sublattices A and B, and cosine-like energy bands associated with the sublattices intersect at zero E near the edges of the Brillouin zone, giving rise to conical sections of the energy spectrum for |E| < 1 eV (Fig. 3). We emphasize that the linear spectrum E = ħνFk is not the only essential feature of the band structure. Indeed, electronic states near zero E (where the bands intersect) are composed of states belonging to the diff erent sublattices, and their relative contributions in the make-up of quasiparticles have to be taken into account by, for example, using two-component wavefunctions (spinors). Th is requires an index to indicate sublattices A and B, which is similar to the spin index (up and down) in QED and, therefore, is referred to as pseudospin. Accordingly, in the formal description of graphene’s quasiparticles by the Dirac-like hamiltonian above, σ refers to pseudospin rather than the real spin of electrons (the latter must be described by additional terms in the hamiltonian). Importantly, QED-specifi c phenomena are oft en inversely proportional to the speed of light c, and therefore enhanced in graphene by a factor c/vF ≈ 300. In particular, this means that pseudospin-related eff ects should generally dominate those due to the real spin. By analogy with QED, one can also introduce a quantity called chirality6 that is formally a projection of σ on the direction of motion k and is positive (negative) for electrons (holes). In essence, chirality in graphene signifi es the fact that k electron and –k hole states are intricately connected because they originate from the same carbon sublattices. Th e concepts of chirality and pseudospin are important because many electronic processes in graphene can be understood as due to conservation of these quantities6,43–48. It is interesting to note that in some narrow-gap 3D semiconductors, the gap can be closed by compositional changes or by applying high pressure. Generally, zero gap does not necessitate Dirac fermions (that imply conjugated electron and hole states), but in some cases they might appear5. Th e diffi culties of tuning the gap to zero, while keeping carrier mobilities high, the lack of possibility to control electronic properties of 3D materials by the electric fi eld eff ect and, generally, less pronounced quantum eff ects in 3D limited studies of such semiconductors mostly to measuring the concentration dependence of their eff ective masses m (for a review, see ref. 49). It is tempting to have a fresh look at zero-gap bulk semiconductors, especially because Dirac fermions have recently been reported even in such a well-studied (small-overlap) 3D material as graphite50,51. CHIRAL QUANTUM HALL EFFECTS At this early stage, the main experimental eff orts have been focused on the electronic properties of graphene, trying to understand the consequences of its QED-like spectrum. Among the most spectacular phenomena reported so far,