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

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疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

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

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

The quantum Hall (QH) effect in two-dimensional electrons and holes in high quality graphene samples is studied in strong magnetic fields up to 45 T. QH plateaus at filling factors nu = 0, +/-1, +/-4 are discovered at magnetic fields B > 20 T, indicating the lifting of the fourfold degeneracy of the previously observed QH states at nu = +/-4(absolute value(n) + 1/2), where n is the Landau-level index. In particular, the presence of the nu = 0, +/-1 QH plateaus indicates that the Landau level at the charge neutral Dirac point splits into four sublevels, lifting sublattice and spin degeneracy. The QH effect at nu = +/-4 is investigated in a tilted magnetic field and can be attributed to lifting of the spin degeneracy of the n = 1 Landau level.

Landau-level splitting in graphene in high magnetic fields.

Z. Jiang, 2, ∗ Y. Zhang, H. L. Stormer, 3, 4 and P. Kim Department of Physics, Columbia University, New York, New York 10027, USA National High Magnetic Field Laboratory, Tallahassee, Florida 32310, USA Department of Applied Physics and Applied Mathematics, Columbia University, New York, New York 10027, USA Bell Laboratories, Alcatel-Lucent, Murray Hill, New Jersey 07974, USA (Dated: February 1, 2008)

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The Nature of Quantum Hall States near the Charge Neutral Dirac Point in Graphene

Neutral spin texture (ST) excitations at $\ensuremath{\nu}=1/3$ are directly observed for the first time by resonant inelastic light scattering. They are determined to involve two simultaneous spin flips. At low magnetic fields, the ST energy is below that of the magnetoroton minimum. With increasing in-plane magnetic field these mode energies cross at a critical ratio of the Zeeman and Coulomb energies of ${\ensuremath{\eta}}_{c}=0.020\ifmmode\pm\else\textpm\fi{}0.001$. Surprisingly, the intensity of the ST mode grows with temperature in the range in which the magnetoroton modes collapse. The temperature dependence is interpreted in terms of a competition between coexisting phases supporting different excitations. We consider the role of the ST excitations in activated transport at $\ensuremath{\nu}=1/3$.

Spin Texture and Magnetoroton Excitations at ν = 1 / 3

We determine the spin susceptibility $\ensuremath{\chi}$ in the weak interaction regime of a tunable, high quality, two-dimensional electron system in a $\mathrm{Ga}\mathrm{As}∕\mathrm{Al}\mathrm{Ga}\mathrm{As}$ heterostructure The band structure effects, modifying mass and $g$-factor, are carefully taken into accounts since they become appreciable for the large electron densities of the weak interaction regime When properly normalized, $\ensuremath{\chi}$ decreases monotonically from 3 to 11 with increasing density over our experimental range from 01 to $4\ifmmode\times\else\texttimes\fi{}{10}^{11}\phantom{\rule{03em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$ In the high density limit, $\ensuremath{\chi}$ tends correctly towards $\ensuremath{\chi}\ensuremath{\rightarrow}1$ and compare well with recent theory

Y.-W. Tan

Papers

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

Landau-level splitting in graphene in high magnetic fields.

The Nature of Quantum Hall States near the Charge Neutral Dirac Point in Graphene

Spin Texture and Magnetoroton Excitations at ν = 1 / 3

Spin susceptibility of a two-dimensional electron system in GaAs towards the weak interaction region