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

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

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

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

Topological insulators are new states of quantum matter which cannot be adiabatically connected to conventional insulators and semiconductors. They are characterized by a full insulating gap in the bulk and gapless edge or surface states which are protected by time-reversal symmetry. These topological materials have been theoretically predicted and experimentally observed in a variety of systems, including HgTe quantum wells, BiSb alloys, and Bi2Te3 and Bi2Se3 crystals. Theoretical models, materials properties, and experimental results on two-dimensional and three-dimensional topological insulators are reviewed, and both the topological band theory and the topological field theory are discussed. Topological superconductors have a full pairing gap in the bulk and gapless surface states consisting of Majorana fermions. The theory of topological superconductors is reviewed, in close analogy to the theory of topological insulators.

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Topological insulators and superconductors

Recent lattice dynamics studies of trans (CH)x and (CD)x are reviewed. The calculations employ a force field which describes both the short range covalent bonds and longer range interactions due to indirect couplings through the π electron system. For the ideal chain, the model yields a good description of the long wavelength optical modes observed in Raman scattering. For chains containing a soliton, a spectrum of localized and resonant defect modes is obtained. The optical activity calculated for the soliton provides a remarkably complete description of the reported dopant induced infrared activity in (CH)x and (CD)x. The effect of a pinning potential on the absorption anticipated in the far infrared is discussed.

Phonons in Ideal and “Kinked” Polyacetylene Chains

Domain walls separating regions of AB and BA interlayer stacking in bilayer graphene have attracted attention as novel examples of structural solitons, topological electronic boundaries, and nanoscale plasmonic scatterers. We show that strong coupling of domain walls to surface plasmons observed in infrared nanoimaging experiments is due to topological chiral modes confined to the walls. The optical transitions among these chiral modes and the band continua enhance the local conductivity, which leads to plasmon reflection by the domain walls. The imaging reveals two kinds of plasmonic standing-wave interference patterns, which we attribute to shear and tensile domain walls. We compute the electronic structure of both wall varieties and show that the tensile wall contains additional confined bands which produce a structure-specific contrast of the local conductivity, in agreement with the experiment. The coupling between the confined modes and the surface plasmon scattering unveiled in this work is expecte...

Plasmon reflections by topological electronic boundaries in bilayer graphene

Phonon dispersion at the Be(0001) surface.

Electronic excitation spectra of graphite substitutionally doped with boron to a level of 0.5 at.% were measured by inelastic electron scattering spectroscopy. In comparison with similar spectra obtained from pristine graphite, new absorption appears in the valence region from 0.2 to 1.5 eV and in the core region near 284 eV due to the lowering of the graphite Fermi level. A tight-binding representation of the three-dimensional graphite band structure is constructed and used to compute the longitudinal dielectric function in the random-phase approximation, including local-field effects. This calculation identifies the new valence absorption as the predecessor of the strong "intraband" plasmon which is observed in acceptor intercalation compounds when more charge is depleted from the graphite planes. The analysis of both core and valence excitations indicates that the Fermi level is lowered by 0.2 eV in borondoped graphite and that the fractional ionization of the boron is 0.8.

Electronic excitations in boron-doped graphite

We report results of tight binding calculation for ordered half monolayer coverages of Al on GaAs(110) in a variety of chemisorption configurations. We find that differences between the chemisorption geometries and relaxations of these configurations lead to a variety of electrical characteristics of the surfaces. The relation of this result to the barrier formed at higher coverages is discussed.

Eugene J. Mele

Papers

Phonons in Ideal and “Kinked” Polyacetylene Chains

Plasmon reflections by topological electronic boundaries in bilayer graphene

Phonon dispersion at the Be(0001) surface.

Electronic excitations in boron-doped graphite

Electronic structure of Al chemisorbed on GaAs(110)