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.

The rise of graphene

This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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The electronic properties of graphene

Two-dimensional materials are attractive for use in next-generation nanoelectronic devices because, compared to one-dimensional materials, it is relatively easy to fabricate complex structures from them. The most widely studied two-dimensional material is graphene, both because of its rich physics and its high mobility. However, pristine graphene does not have a bandgap, a property that is essential for many applications, including transistors. Engineering a graphene bandgap increases fabrication complexity and either reduces mobilities to the level of strained silicon films or requires high voltages. Although single layers of MoS(2) have a large intrinsic bandgap of 1.8 eV (ref. 16), previously reported mobilities in the 0.5-3 cm(2) V(-1) s(-1) range are too low for practical devices. Here, we use a halfnium oxide gate dielectric to demonstrate a room-temperature single-layer MoS(2) mobility of at least 200 cm(2) V(-1) s(-1), similar to that of graphene nanoribbons, and demonstrate transistors with room-temperature current on/off ratios of 1 × 10(8) and ultralow standby power dissipation. Because monolayer MoS(2) has a direct bandgap, it can be used to construct interband tunnel FETs, which offer lower power consumption than classical transistors. Monolayer MoS(2) could also complement graphene in applications that require thin transparent semiconductors, such as optoelectronics and energy harvesting.

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Single-layer MoS2 transistors

We report the measurement of the thermal conductivity of a suspended single-layer graphene. The room temperature values of the thermal conductivity in the range ∼(4.84 ± 0.44) × 103 to (5.30 ± 0.48) × 103 W/mK were extracted for a single-layer graphene from the dependence of the Raman G peak frequency on the excitation laser power and independently measured G peak temperature coefficient. The extremely high value of the thermal conductivity suggests that graphene can outperform carbon nanotubes in heat conduction. The superb thermal conduction property of graphene is beneficial for the proposed electronic applications and establishes graphene as an excellent material for thermal management.

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Superior Thermal Conductivity of Single-Layer Graphene

The remarkable mechanical properties of carbon nanotubes arise from the exceptional strength and stiffness of the atomically thin carbon sheets (graphene) from which they are formed. In contrast, bulk graphite, a polycrystalline material, has low fracture strength and tends to suffer failure either by delamination of graphene sheets or at grain boundaries between the crystals. Now Stankovich et al. have produced an inexpensive polymer-matrix composite by separating graphene sheets from graphite and chemically tuning them. The material contains dispersed graphene sheets and offers access to a broad range of useful thermal, electrical and mechanical properties. Individual sheets of graphene can be readily incorporated into a polymer matrix, giving rise to composite materials having potentially useful electronic properties. Graphene sheets—one-atom-thick two-dimensional layers of sp2-bonded carbon—are predicted to have a range of unusual properties. Their thermal conductivity and mechanical stiffness may rival the remarkable in-plane values for graphite (∼3,000 W m-1 K-1 and 1,060 GPa, respectively); their fracture strength should be comparable to that of carbon nanotubes for similar types of defects1,2,3; and recent studies have shown that individual graphene sheets have extraordinary electronic transport properties4,5,6,7,8. One possible route to harnessing these properties for applications would be to incorporate graphene sheets in a composite material. The manufacturing of such composites requires not only that graphene sheets be produced on a sufficient scale but that they also be incorporated, and homogeneously distributed, into various matrices. Graphite, inexpensive and available in large quantity, unfortunately does not readily exfoliate to yield individual graphene sheets. Here we present a general approach for the preparation of graphene-polymer composites via complete exfoliation of graphite9 and molecular-level dispersion of individual, chemically modified graphene sheets within polymer hosts. A polystyrene–graphene composite formed by this route exhibits a percolation threshold10 of ∼0.1 volume per cent for room-temperature electrical conductivity, the lowest reported value for any carbon-based composite except for those involving carbon nanotubes11; at only 1 volume per cent, this composite has a conductivity of ∼0.1 S m-1, sufficient for many electrical applications12. Our bottom-up chemical approach of tuning the graphene sheet properties provides a path to a broad new class of graphene-based materials and their use in a variety of applications.

Graphene-based composite materials

When electrons are confined in two-dimensional materials, quantum-mechanically enhanced transport phenomena such as the quantum Hall effect can be observed. Graphene, consisting of an isolated single atomic layer of graphite, is an ideal realization of such a two-dimensional system. However, its behaviour is expected to differ markedly from the well-studied case of quantum wells in conventional semiconductor interfaces. This difference arises from the unique electronic properties of graphene, which exhibits electron–hole degeneracy and vanishing carrier mass near the point of charge neutrality1,2. Indeed, a distinctive half-integer quantum Hall effect has been predicted3,4,5 theoretically, as has the existence of a non-zero Berry's phase (a geometric quantum phase) of the electron wavefunction—a consequence of the exceptional topology of the graphene band structure6,7. Recent advances in micromechanical extraction and fabrication techniques for graphite structures8,9,10,11,12 now permit such exotic two-dimensional electron systems to be probed experimentally. Here we report an experimental investigation of magneto-transport in a high-mobility single layer of graphene. Adjusting the chemical potential with the use of the electric field effect, we observe an unusual half-integer quantum Hall effect for both electron and hole carriers in graphene. The relevance of Berry's phase to these experiments is confirmed by magneto-oscillations. In addition to their purely scientific interest, these unusual quantum transport phenomena may lead to new applications in carbon-based electronic and magneto-electronic devices.

https://arxiv.org/pdf/cond-mat/0509355.pdf

Experimental observation of the quantum Hall effect and Berry's phase in graphene

In the present study, a scanning tunneling microscope (STM), modified to include active lateral position feedback control, is employed to image single and few layer graphene films placed on a nonconductive substrate under ambient conditions. The return path for tunneling electrons was provided by gold electrodes produced by either electron beam lithography or shadow evaporation techniques. STM images of graphene films with a thickness of two or more layers display topographs that are similar to those obtained from a bulk graphite crystal. For single layer graphene sheets, the ability to obtain atomically resolved images was found to be extremely sensitive to sample preparation methods. Graphene microdevices produced by electron beam lithography with edges covered by gold electrodes show hexagonal patterns similar to those obtained from ultrahigh vacuum STM images reported earlier. Ambient STM measurements of graphene microdevices made by shadow mask evaporation, whose edges were exposed to air, exhibited ...

Yuanbo Zhang

Papers

Experimental observation of the quantum Hall effect and Berry's phase in graphene

Scanning Tunneling Microscope Studies of Ultrathin Graphitic (Graphene) Films on an Insulating Substrate under Ambient Conditions