Applications of Graphene (original) (raw)

The electronic properties 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 ͑surface͒ states in graphene depend on the edge termination ͑zigzag or armchair͒ 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.

Graphene: synthesis and applications

The low energy bandstructure of graphene involves its π electrons. The first bandstructure calculations were performed in 1947 by P.R. Wallace 1 and the bandstructure is shown in Fig. 1a. The valence band is formed by bonding π states, while the conduction band is formed by the anti-bonding π* states. These states are orthogonal; there is no avoided crossing, and valence and conduction bands touch at six points, the so-called Dirac points. Two of these points are independent and are indicated in Fig. 1a as the K and K' points. For energies below about 1 eV, which are relevant in most electrical transport properties, the bandstructure can be approximated by two symmetric cones representing valence and conduction bands touching at the Dirac point. Electron dispersion in this energy region is to a large extent linear, similar to that of light and unlike other conventional 2D systems with parabolic dispersion 2-8. This linear dispersion has profound implications regarding the properties of graphene. Also, unlike the conventional 2D electron systems, which are usually formed at buried semiconductor interfaces, graphene is a single atomic layer directly accessible to experimental observation, but also very susceptible to external perturbations which can interact directly with its π-electron system. The unit cell of graphene contains two carbon atoms and the graphene lattice can be viewed as formed by two sub-lattices, A and B, evolving from these two atoms (see Fig. 1b). The electronic Hamiltonian describing the low energy electronic structure of graphene can then be written in the form of a relativistic Dirac Hamiltonian: H = v F σ⋅h-k, where σ is a spinor-like wavefunction, v F is the Fermi velocity of graphene, and k the wavevector of the electron 2-8. However, the spinor character of the graphene wavefunction arises not from spin, but from the fact that there are two atoms in the unit cell. We can define a pseudo-spin that has the same direction as the group velocity and describes the electron population in the A and B sites. As with real spin, pseudo-spin reversal is not allowed during carrier interactions. This underlies the inhibition of Graphene, since the demonstration of its easy isolation by the exfoliation of graphite in 2004 by Novoselov, Geim and co-workers , has been attracting enormous attention in the scientific community. Because of its unique properties, high hopes have been placed on it for technological applications in many areas. Here we will briefly review aspects of two of these application areas: analog electronics and photonics/optoelectronics. We will discuss the relevant material properties, device physics, and some of the available results. Of course, we cannot rely on graphite exfoliation as the source of graphene for technological applications, so we will start by introducing large scale graphene growth techniques.

Electronic properties of graphene

2007

Graphene is the first example of truly two-dimensional crystals-it's just one layer of carbon atoms. It turns out that graphene is a gapless semiconductor with unique electronic properties resulting from the fact that charge carriers in graphene obey linear dispersion relation, thus mimicking massless relativistic particles. This results in the observation of a number of very peculiar electronic properties-from an anomalous quantum Hall effect to the absence of localization. It also provides a bridge between condensed matter physics and quantum electrodynamics and opens new perspectives for carbon-based electronics.

Properties of graphene: a theoretical perspective

Advances in Physics, 2010

The electronic properties of graphene, a two-dimensional crystal of carbon atoms, are exceptionally novel. For instance the low-energy quasiparticles in graphene behave as massless chiral Dirac fermions which has led to the experimental observation of many interesting effects similar to those predicted in the relativistic regime. Graphene also has immense potential to be a key ingredient of new devices such as single molecule gas sensors, ballistic transistors, and spintronic devices. Bilayer graphene, which consists of two stacked monolayers and where the quasiparticles are massive chiral fermions, has a quadratic low-energy band structure which generates very different scattering properties from those of the monolayer. It also presents the unique property that a tunable band gap can be opened and controlled easily by a top gate. These properties have made bilayer graphene a subject of intense interest.

Physical properties of graphene nano-devices

In this doctoral thesis the two dimensional material graphene has been studied in depth with particular respect to Zener tunnelling devices. From the hexagonal structure the Hamiltonian at a Dirac point was derived with the option of including an energy gap. This Hamiltonian was then used to obtain the tunnelling properties of various graphene nano-devices; the devices studied include Zener tunnelling potential barriers such as single and double graphene potential steps. A form of the Landauer formalism was obtained for graphene devices. Combined with the scattering properties of potential barriers the current and conductance was found for a wide range of graphene nano-devices. These results were then compared to recently obtained experimental results for graphene nanoribbons, showing many similarities between nanoribbons and infinite sheet graphene. The methods studied were then applied to materials which have been shown to possess three dimensional Dirac cones known as topological insulators. In the case of Cd3As2 the Dirac cone is asymmetrical with respect to the z direction, the effect of this asymmetry has been discussed with comparison to the symmetrical case.

Graphene Review

This review examines the properties of graphene from an experimental perspective. The intent is to review the most important experimental results at a level of detail appropriate for new graduate students who are interested in a general overview of the fascinating properties of graphene. While some introductory theoretical concepts are provided, including a discussion of the electronic band structure and phonon dispersion, the main emphasis is on describing relevant experiments and important results as well as some of the novel applications of graphene. In particular, this review covers graphene synthesis and characterization, field-effect behavior, electronic transport properties, magneto-transport, integer and fractional quantum Hall effects, mechanical properties, transistors, optoelectronics, graphene-based sensors, and biosensors. This approach attempts to highlight both the means by which the current understanding of graphene has come about and some tools for future contributions.

Materials Today Magazine - Sarkar - Covalent Chemistry in Graphene Electronics

Materials Today

The new carbon age 1 , which is the third wave in the carbon revolution, has witnessed overwhelming interest in low-dimensional carbon materials, with particular attention to graphene, the newest member of the series of carbon allotropes. This two-dimensional form of pure sp 2 hybridized carbon -a giant molecule 2 of atomic thickness -has garnered tremendous attention among both physicists and chemists and has provided a test-bed for fundamental and device physics 3,4 , and a unique chemical substrate 5-9 . In line with theoretical predictions, charge carriers in graphene behave like massless Dirac fermions, which is a direct consequence of the linear energy dispersion relation 10 . Such features serve to support the use of graphene for mechanical, thermal, electronic, magnetic, and optical applications, but the absence of a band-gap in graphene makes it unsuitable for conventional field effect transistors (FETs) 11,12 , and its lack of solution processability remains to be resolved 13 . These issues are potentially amenable to solution by chemical techniques, but the effect of chemistry on the mobility of functionalized graphene devices is an imposing challenge 14 . Dimensionality defines the physical and chemical behavior of a material and distinguishes one material from the other even among those of the same chemical composition 15 ; while the chemical concepts of structure and hybridization lead to the same conclusion 16-18 . From the standpoint of both physics and chemistry, the two-dimensional (2D) graphene materials with atomically flat surface are remarkably different from that of the quasi-zero-dimensional (0D) fullerenes, and the onedimensional (1D) carbon nanotube materials. The experimental isolation