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

Raman spectroscopy is an integral part of graphene research. It is used to determine the number and orientation of layers, the quality and types of edge, and the effects of perturbations, such as electric and magnetic fields, strain, doping, disorder and functional groups. This, in turn, provides insight into all sp(2)-bonded carbon allotropes, because graphene is their fundamental building block. Here we review the state of the art, future directions and open questions in Raman spectroscopy of graphene. We describe essential physical processes whose importance has only recently been recognized, such as the various types of resonance at play, and the role of quantum interference. We update all basic concepts and notations, and propose a terminology that is able to describe any result in literature. We finally highlight the potential of Raman spectroscopy for layered materials other than graphene.

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Raman spectroscopy as a versatile tool for studying the properties of graphene

Raman spectroscopy in graphene

Every few years, a new material with unique properties emerges and fascinates the scientific community, typical recent examples being high-temperature superconductors and carbon nanotubes. Graphene is the latest sensation with unusual properties, such as half-integer quantum Hall effect and ballistic electron transport. This two-dimensional material which is the parent of all graphitic carbon forms is strictly expected to comprise a single layer, but there is considerable interest in investigating two-layer and few-layer graphenes as well. Synthesis and characterization of graphenes pose challenges, but there has been considerable progress in the last year or so. Herein, we present the status of graphene research which includes aspects related to synthesis, characterization, structure, and properties.

Graphene: The New Two-Dimensional Nanomaterial

We present the science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems, targeting an evolution in technology, that might lead to impacts and benefits reaching into most areas of society. This roadmap was developed within the framework of the European Graphene Flagship and outlines the main targets and research areas as best understood at the start of this ambitious project. We provide an overview of the key aspects of graphene and related materials (GRMs), ranging from fundamental research challenges to a variety of applications in a large number of sectors, highlighting the steps necessary to take GRMs from a state of raw potential to a point where they might revolutionize multiple industries. We also define an extensive list of acronyms in an effort to standardize the nomenclature in this emerging field.

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Science and technology roadmap for graphene, related two-dimensional crystals, and hybrid systems

The electronic structure of bilayer graphene is investigated from a resonant Raman study of the ${G}^{\ensuremath{'}}$ band using different laser excitation energies. The values of the parameters of the Slonczewski-Weiss-McClure model for bilayer graphene are obtained from the analysis of the dispersive behavior of the Raman features, and reveal the difference of the effective masses of electrons and holes. The splitting of the two TO phonon branches in bilayer graphene is also obtained from the experimental data. Our results have implications for bilayer graphene electronic devices.

Probing the electronic structure of bilayer graphene by Raman scattering

Raman spectroscopy was used to determine the dispersion of the longitudinal acoustic (LA) and in-plane transverse optic phonon branches near the Dirac $K$ point of monolayer graphene from the analysis of the dispersion of two second-order Raman peaks involving the LA and TO phonons. We show that the velocities of the phonons involved in the double resonance Raman process are given by ${v}_{\mathit{LA}}=7.70\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{v}_{F}$ and ${v}_{\mathit{TO}}=5.47\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}{v}_{F}$, where ${v}_{F}$ is the Fermi velocity of the associated electrons. The experimental results for the phonon dispersion in monolayer graphene are compared with those for turbostratic graphite and also with different theoretical models.

Determination of LA and TO phonon dispersion relations of graphene near the Dirac point by double resonance Raman scattering

Magnetic field studies of elastic scattering and optic-phonon emission in resonant-tunneling devices.

A Raman study of a back gated bilayer graphene sample is presented. The changes in the Fermi level induced by charge transfer splits the Raman G band, hardening its higher component and softening the lower one. These two components are associated with the symmetric (S) and antisymmetric vibration (AS) of the atoms in the two layers, the later one becoming Raman active due to inversion symmetry breaking. The phonon hardening and softening are explained by considering the selective coupling of the S and AS phonons with interband and intraband electron-hole pairs.

Observation of Distinct Electron-Phonon Couplings in Gated Bilayer Graphene

We report the first unambiguous observation of intrinsic bistability due to space charge build-up in an asymmetric GaAs/(AlGa)As double-barrier resonant tunnelling device.

E. S. Alves

Papers

Probing the electronic structure of bilayer graphene by Raman scattering

Determination of LA and TO phonon dispersion relations of graphene near the Dirac point by double resonance Raman scattering

Magnetic field studies of elastic scattering and optic-phonon emission in resonant-tunneling devices.

Observation of Distinct Electron-Phonon Couplings in Gated Bilayer Graphene

Observation of intrinsic bistability in resonant tunnelling devices