# 摘要

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.

# 前言

Graphene is the name given to a flat 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. Theoretically, graphene (or ‘2D graphite’) has been studied for sixty years,[1–3] 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 electrodynamics,[4–6] 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’ material[5] 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 ago[7,8] — and especially when the follow-up experiments[9,10] confirmed that its charge carriers were indeed massless Dirac fermions. So, the graphene ‘gold rush’ has begun.

# 原本不应该存在的材料

More than 70 years ago, Landau and Peierls argued that strictly 2D crystals were thermodynamically unstable and could not exist.[11,12] Their theory pointed out that a divergent contribution of thermal fluctuations in low-dimensional crystal lattices should lead to such displacements of atoms that they become comparable to interatomic distances at any finite temperature.[13] The argument was later extended by Mermin[14] and is strongly supported by an omnibus of experimental observations. Indeed, the melting temperature of thin films rapidly decreases with decreasing thickness, and the films become unstable (segregate into islands or decompose) at a thickness of, typically, dozens of atomic layers.[15,16] 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 lattices.[15,16] Without such a 3D base, 2D materials were presumed not to exist, until 2004, when the common wisdom was flaunted by the experimental discovery of graphene[7] and other free-standing 2D atomic crystals (for example, single-layer boron nitride and half-layer BSCCO).[8] These crystals could be obtained on top of non-crystalline substrates,[8–10] in liquid suspension[7,17] and as suspended membranes.[18]

70 多年前，Landau 和 Peierls 认为严格意义上的二维晶体是热力学不稳定的，因此不可能存在[11,12]。他们的理论指出，低维晶格中发散分布的热涨落会导致原子的位移，其偏移量可达任何有限的温度下原子间的距离[13]。这一论点后来被 Mermin[14] 所扩展，并得到了实验观察综合结果的有力支持。事实上，薄膜的熔化温度随着厚度的减小而迅速降低，并且薄膜在只有几十个原子层的厚度时会变得不稳定（分离成岛状或分解）[15,16]。因此，原子单层迄今为止仅被认为是更大的 3D 结构的一个组成部分，通常外延生长在具有匹配晶格的单晶顶部[15,16]。人们推测，如果没有这样的 3D 基底，2D 材料是不存在的。直到 2004 年，在实验中发现石墨烯[7]和其他独立的二维原子晶体（如单层氮化硼和半层 BSCCO）刷新了人们的认知[8]。这些晶体可以在非晶衬底[8–10]，液体悬浮液[7,17]上作为悬浮薄膜获得。

Importantly, the 2D crystals were found not only to be continuous but to exhibit high crystal quality.[7–10,17,18] The latter is most obvious for the case of graphene, in which charge carriers can travel thousands of interatomic distances without scattering.[7–10] With the benefit 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 ($\ll 1\ \rm{mm}$) and strong interatomic bonds ensure that thermal fluctuations cannot lead to the generation of dislocations or other crystal defects even at elevated temperature.[13,14] A complementary viewpoint is that the extracted 2D crystals become intrinsically stable by gentle crumpling in the third dimension[18,19] (for an artist’s impression of the crumpling, see the cover of this issue). Such 3D warping (observed on a lateral scale of $\approx 10\ \rm{nm}$)[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 energy.[19]

# 石墨烯简史

Before reviewing the earlier work on graphene, it is useful to define what 2D crystals are. Obviously, a single atomic plane is a 2D crystal, whereas $100$ layers should be considered as a thin film 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 layers.[20] 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 appear,[7,21] and the conduction and valence bands start notably overlapping.[7,20] This allows single-, double- and few- ($3$ to $\lt 10$) layer graphene to be distinguished as three diff erent types of 2D crystals (‘graphenes’). Thicker structures should be considered, to all intents and purposes, as thin films of graphite. From the experimental point of view, such a definition is also sensible. The screening length in graphite is only $\approx 5\ \mathring{\rm{A}}$ (that is, less than two layers in thickness)[21] and, hence, one must differentiate between the surface and the bulk even for films as thin as five layers.[21,22]

Earlier attempts to isolate graphene concentrated on chemical exfoliation. To this end, bulk graphite was first intercalated[23] so that graphene planes became separated by layers of intervening atoms or molecules. Th is usually resulted in new 3D materials.[223] 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 sheets.[24–26] Because of its uncontrollable character, graphitic sludge has so far attracted only limited interest.

There 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 films thicker than $\approx 100$ layers.[27] On the other hand, single- and few-layer graphene have been grown epitaxially by chemical vapour deposition of hydrocarbons on metal substrates[28,29] and by thermal decomposition of SiC (refs [30–34]). Such films 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 carriers.[32,33] Epitaxial growth of graphene offers probably the only viable route towards electronic applications and, with so much at stake, rapid progress in this direction is expected. The approach that seems promising but has not been attempted yet is the use of the previously demonstrated epitaxy on catalytic surfaces[28,29] (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.