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

There are two possible terminations for the ideal NiAl(111) surface, i.e., all Al or all Ni on the surface atomic layer. We investigate which termination occurs on the NiAl(111) surface by comparing the pseudopotential electronic band structure of a Ni-terminated and an Al-terminated NiAl(111) surface with the angle-resolved photoemission data on a NiAl(111) sample. The measured surface band structure shares common features partly with that of the Ni termination and also partly with that of the Al termination, which supports the theory that the real NiAl(111) surface is composed of both Ni- and Al-terminated (111) domains, as suggested by a recent low-energy electron diffraction (LEED) study. We also determine the relaxation of the two outermost atomic layers for both terminations by the pseudopotential total-energy calculations and compare them with the LEED results. We find that the present results are in good agreement with the LEED analysis for Ni termination, but in qualitative disagreement for Al termination.

Atomic and electronic structure of the NiAl(111) surface

We report on a theoretical analysis of the Floquet topological crystalline phases in driven one-dimensional photonic crystals mediated by second-order optical nonlinearity. We define the photonic Berry connection and photonic polarization in such systems using different methods and prove their equivalence. We present two examples of topological phase transitions in which two Floquet bands cross and open new gaps under the driving field. Finally, we analyze the physical consequences of each topological phase transition by examining edge states and filling anomalies. Our study presents routes toward the realization of robust reconfigurable photonic cavities with topologically protected light confinement.

Floquet Topological Phases in One-Dimensional Nonlinear Photonic Crystals.

Dynamical conductivity in polyacetylene

We consider an anisotropic planar-rotor model on a two-dimensional triangular lattice to model the dopant ordering in polyacetylene in the process of alkali-metal doping. With the combination of a Ginzberg-Landau expansion of the free energy close to the critical temperature and total-energy calculations at zero temperature, we obtain a phase diagram in the plane of temperature and alkali-metal chemical potential, which shows various modulated phases which appear in the process of alkali-metal doping of the polymer. These results are compared with experimental observations by Winokur et al. [Phys. Rev. Lett. 58, 2329 (1987)].

Eugene J. Mele

Papers

Atomic and electronic structure of the NiAl(111) surface

Floquet Topological Phases in One-Dimensional Nonlinear Photonic Crystals.

Dynamical conductivity in polyacetylene

Doping-induced structural phase transition in polyacetylene.

Electronic structure of the zinc-blende and rocksalt phases of InSb