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

Titanium Dioxide Nanomaterials: Synthesis, Properties, Modifications, and Applications

Thermoelectric materials, which can generate electricity from waste heat or be used as solid-state Peltier coolers, could play an important role in a global sustainable energy solution. Such a development is contingent on identifying materials with higher thermoelectric efficiency than available at present, which is a challenge owing to the conflicting combination of material traits that are required. Nevertheless, because of modern synthesis and characterization techniques, particularly for nanoscale materials, a new era of complex thermoelectric materials is approaching. We review recent advances in the field, highlighting the strategies used to improve the thermopower and reduce the thermal conductivity.

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Complex thermoelectric materials.

CARBON nanotubes1 are expected to have a wide variety of interesting properties. Capillarity in open tubes has already been demonstrated2–5, while predictions regarding their electronic structure6–8 and mechanical strength9 remain to be tested. To examine the properties of these structures, one needs tubes with well defined morphologies, length, thickness and a number of concentric shells; but the normal carbon-arc synthesis10,11 yields a range of tube types. In particular, most calculations have been concerned with single-shell tubes, whereas the carbon-arc synthesis produces almost entirely multi-shell tubes. Here we report the synthesis of abundant single-shell tubes with diameters of about one nanometre. Whereas the multi-shell nanotubes are formed on the carbon cathode, these single-shell tubes grow in the gas phase. Electron diffraction from a single tube allows us to confirm the helical arrangement of carbon hexagons deduced previously for multi-shell tubes1.

Single-shell carbon nanotubes of 1-nm diameter

The surface science of titanium dioxide

The electronic structures of some possible carbon fibers nucleated from the hemisphere of a ${\mathrm{C}}_{60}$ molecule are presented. A one-dimensional electronic band-structure model of such carbon fibers, having not only rotational symmetry but also screw axes, is derived by folding the two-dimensional energy bands of graphite. A simple tight-binding model shows that some fibers are metallic and are stable against perturbations of the one-dimensional energy bands and the mixing of \ensuremath{\sigma} and \ensuremath{\pi} bands due to the curvature of the circumference of the fiber.

Electronic structure of graphene tubules based on C 60

The basic concepts and characteristics of Raman spectra from carbon nanotubes (both isolated and bundled) are presented. The general characteristics of the radial breathing mode, tangential mode (G band), disorder-induced mode (D-band) and other Raman features are presented, with the focus directed toward their use for carbon nanotube characterization. Polarization analysis, surface enhanced Raman spectroscopy and complementary optical techniques are also discussed in terms of their advantages and limitations.

https://iopscience.iop.org/article/10.1088/1367-2630/5/1/139/pdf

Characterizing carbon nanotube samples with resonance Raman scattering

Efficient solid state energy conversion based on the Peltier effect for cooling and the Seebeck effect for power generation calls for materials with high electrical conductivity σ, high Seebeck coefficient S, and low thermal conductivity k. Identifying materials with a high thermoelectric figure of merit Z(= S2σ/k) has proven to be an extremely challenging task. After 30 years of slow progress, thermoelectric materials research experienced a resurgence, inspired by the developments of new concepts and theories to engineer electron and phonon transport in both nanostructures and bulk materials. This review provides a critical summary of some recent developments of new concepts and new materials. In nanostructures, quantum and classical size effects provide opportunities to tailor the electron and phonon transport through structural engineering. Quantum wells, superlattices, quantum wires, and quantum dots have been employed to change the band structure, energy levels, and density of states of elect...

Recent developments in thermoelectric materials

This paper reviews progress that has been made in the use of Raman spectroscopy to study graphene and carbon nanotubes These are two nanostructured forms of sp2 carbon materials that are of major current interest These nanostructured materials have attracted particular attention because of their simplicity, small physical size and the exciting new science they have introduced This review focuses on each of these materials systems individually and comparatively as prototype examples of nanostructured materials In particular, this paper discusses the power of Raman spectroscopy as a probe and a characterization tool for sp2 carbon materials, with particular emphasis given to the field of photophysics Some coverage is also given to the close relatives of these sp2 carbon materials, namely graphite, a three-dimensional (3D) material based on the AB stacking of individual graphene layers, and carbon nanoribbons, which are one-dimensional (1D) planar structures, where the width of the ribbon is on the nano

Raman spectroscopy of graphene and carbon nanotubes

We report femtosecond time-resolved pump-probe reflection experiments in semimetals and semiconductors that show large-amplitude oscillations with periods characteristic of lattice vibrations. Only ${\mathit{A}}_{1}$ modes are detected, although modes with other symmetries are observed with comparable intensity in Raman scattering. We present a theory of the excitation process in this class of materials, which we refer to as displacive excitation of coherent phonons (DECP). In DECP, after excitation by a pump pulse, the electronically excited system rapidly comes to quasiequilibrium in a time short compared to nuclear response times. In materials with ${\mathit{A}}_{1}$ vibrational modes, the quasiequilibrium nuclear ${\mathit{A}}_{1}$ coordinates are displaced with no change in lattice symmetry, giving rise to a coherent vibration of ${\mathit{A}}_{1}$ symmetry about the displaced quasiequilibrium coordinates. One important prediction of the DECP mechanism is the excitation of only modes with ${\mathit{A}}_{1}$ symmetry. Furthermore, the oscillations in the reflectivity R are excited with a cos(${\mathrm{\ensuremath{\omega}}}_{0}$t) dependence, where t=0 is the time of arrival of the pump pulse peak, and ${\mathrm{\ensuremath{\omega}}}_{0}$ is the vibrational frequency of the ${\mathit{A}}_{1}$ mode. These predictions agree well with our observations in Bi, Sb, Te, and ${\mathrm{Ti}}_{2}$${\mathrm{O}}_{3}$. The fit of the experimental \ensuremath{\Delta}R(t)/R(0) data to the theory is excellent.

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G. Dresselhaus

Papers

Electronic structure of graphene tubules based on C 60

Characterizing carbon nanotube samples with resonance Raman scattering

Recent developments in thermoelectric materials

Raman spectroscopy of graphene and carbon nanotubes

Theory for displacive excitation of coherent phonons.