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.

/pdf/the-electronic-properties-of-graphene-2siyzsnf5w.pdf

The electronic properties of graphene

Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

/pdf/two-dimensional-gas-of-massless-dirac-fermions-in-graphene-3c7819c4ex.pdf

Two-dimensional gas of massless Dirac fermions in graphene

Single-layer metal dichalcogenides are two-dimensional semiconductors that present strong potential for electronic and sensing applications complementary to that of graphene.

/pdf/electronics-and-optoelectronics-of-two-dimensional-2jbqr1unvw.pdf

Electronics and optoelectronics of two-dimensional transition metal dichalcogenides.

The electronic properties of ultrathin crystals of molybdenum disulfide consisting of N=1,2,…,6 S-Mo-S monolayers have been investigated by optical spectroscopy Through characterization by absorption, photoluminescence, and photoconductivity spectroscopy, we trace the effect of quantum confinement on the material's electronic structure With decreasing thickness, the indirect band gap, which lies below the direct gap in the bulk material, shifts upwards in energy by more than 06 eV This leads to a crossover to a direct-gap material in the limit of the single monolayer Unlike the bulk material, the MoS₂ monolayer emits light strongly The freestanding monolayer exhibits an increase in luminescence quantum efficiency by more than a factor of 10⁴ compared with the bulk material

Atomically thin MoS2: a new direct-gap semiconductor

The electronic properties of inversion and accumulation layers at semiconductor-insulator interfaces and of other systems that exhibit two-dimensional or quasi-two-dimensional behavior, such as electrons in semiconductor heterojunctions and superlattices and on liquid helium, are reviewed. Energy levels, transport properties, and optical properties are considered in some detail, especially for electrons at the (100) silicon-silicon dioxide interface. Other systems are discussed more briefly.

Electronic properties of two-dimensional systems

Because of the chiral nature of electrons in a monolayer of graphite (graphene) one can expect weak antilocalization and a positive weak-field magnetoresistance in it. However, trigonal warping (which breaks $\mathbf{p}\ensuremath{\rightarrow}\ensuremath{-}\mathbf{p}$ symmetry of the Fermi line in each valley) suppresses antilocalization, while intervalley scattering due to atomically sharp scatterers in a realistic graphene sheet or by edges in a narrow wire tends to restore conventional negative magnetoresistance. We show this by evaluating the dependence of the magnetoresistance of graphene on relaxation rates associated with various possible ways of breaking a ``hidden'' valley symmetry of the system.

/pdf/weak-localization-magnetoresistance-and-valley-symmetry-in-5a8tfi205w.pdf

Weak-localization magnetoresistance and valley symmetry in graphene.

A brief review is given of electronic and transport properties of carbon nanotubes obtained mainly in a k · p scheme. The topics include a giant Aharonov–Bohm effect on the band gap and a Landau-level formation in magnetic fields, magnetic properties, interaction effects on the band structure, optical absorption spectra, and exciton effects. Transport properties are also discussed including absence of backward scattering except for scatterers with a potential range smaller than the lattice constant, its extension to multi-channel cases, a conductance quantization in the presence of short-range and strong scatterers such as lattice vacancies, and transport across junctions between nanotubes with different diameters. A continuum model for phonons in the long-wavelength limit and the resistivity determined by phonon scattering are reviewed as well.

/pdf/theory-of-electronic-states-and-transport-in-carbon-9yocmap4w5.pdf

Theory of Electronic States and Transport in Carbon Nanotubes

The static polarization function is calculated in two-dimensional graphite and used for the calculation of the conductivity limited by charged-impurity scattering. The conductivity increases in proportion to the electron concentration and the mobility remains independent of the Fermi energy, in qualitative agreement with experiments. The screening increases in proportion to temperature at sufficiently high temperatures in contrast to the behavior in conventional two-dimensional systems, leading to the mobility increase proportional to the square of temperature.

/pdf/screening-effect-and-impurity-scattering-in-monolayer-4fwwx6il3s.pdf

Screening Effect and Impurity Scattering in Monolayer Graphene

Electron-phonon scattering is studied within an effective-mass theory. A continuum model for acoustic phonons is introduced and electron-phonon interaction due to modification of band structure is derived as well as a normal deformation potential. In a metallic nanotube, the deformation potential does not participate in electron scattering and a metallic nanotube becomes nearly a one-dimensional ballistic conductor even at room temperature. A resistivity determined by small band-structure interaction depends on the chirality at low temperatures. A magnetic field perpendicular to the axis induces electron scattering by the deformation potential, giving rise to huge positive magnetoresistance.

/pdf/phonons-and-electron-phonon-scattering-in-carbon-nanotubes-407w5uykr1.pdf

Tsuneya Ando

Papers

Electronic properties of two-dimensional systems

Weak-localization magnetoresistance and valley symmetry in graphene.

Theory of Electronic States and Transport in Carbon Nanotubes

Screening Effect and Impurity Scattering in Monolayer Graphene

Phonons and electron-phonon scattering in carbon nanotubes