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

Methods for injecting charge currents on single wall molecular nanotubes using nonlinear excitation by optical fields are studied. By varying the relative phases, frequencies and polarizations of the incident fields one can control the symmetries of the optically excited states and the phase space distribution for the photoexcited electrons. We study coherent control of a photocurrent on a carbon nanotube using quantum interference of excitations from optical fields oscillating at ω and 2ω. For BN nanotubes we study the shift current as a probe of the ground state polarization of the heteropolar tube. Here we find that the sign and size of the ground state polarization is an intrinsic quantum effect controlled by the chiral index of the BN nanotube.

Optical current injection in carbon and boron nitride nanotubes

We apply a Hubbard Peierls Hamiltonian to study the spectrum of low lying excitations for conjugated polymers. This study makes use of a renormalization group approach for the many particle Hamiltonian to accurately describe electron correlation effects in the excited states, and also explicitly treats coupling of the electrons to the lattice degrees of freedom. We find that the noninteracting U=0 theories provide a reasonable starting point from which to interpret the excitations; however, the interaction effects are seen play a very important role, introducing an important class of low lying neutral excitations in the structure. The low lying electronic excitations in the model are self trapped triplet excitons, and the low lying singlet excitations are found to include a "bi-exciton" constructed from a bound pair of the low lying triplet excitations.

Excitations in Conjugated Polymers

Orientational ordering and insulator metal transition in doped polyacetylene

The specifics of charge screening and electrostatic potential spatial distribution in multilayered graphene films placed in between charged substrates is theoretically analyzed. It is shown that by varying the areal charge densities on the substrates and/or the thickness of the graphene stack one may tune the doped carriers distribution over the system. When the charge densities on the substrates are weak, the carriers distribution and electrostatic potential profile agree with semimetallic properties of graphene. However, when the amount of the donated charge is sufficiently large the transition to a metallic-like behavior of the graphene layers occurs. The possibilities for experimental observation of the predicted transition are discussed.

Electric charge and potential distribution in twisted multilayer graphene

Scanning tunneling images of carbon nanotubes frequently show electron distributions which break the local sixfold symmetry of the graphene sheet. We present a theory of these images which relates the anisotropies to off diagonal correlations in the single particle density matrix induced by elastic scattering from tube defects. The theory reveals that there are three general effects which one can associate with elastic scattering from defects. Any defect can be characterized by a matrix of reflection coefficients which define its signature in the tunneling image. We provide a theory for tunneling images with broken translational symmetry, “primitive” broken symmetry images with broken rotational symmetry but no broken translational symmetry, and a novel “semiconductor effect” in which the symmetry of the tunneling image switches with the sign of the tunnel bias.

Eugene J. Mele

Papers

Optical current injection in carbon and boron nitride nanotubes

Excitations in Conjugated Polymers

Orientational ordering and insulator metal transition in doped polyacetylene

Electric charge and potential distribution in twisted multilayer graphene

Low Energy Theory for STM Imaging of Carbon Nanotubes