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

Research in the use of organic polymers as the active semiconductors in light-emitting diodes has advanced rapidly, and prototype devices now meet realistic specifications for applications. These achievements have provided insight into many aspects of the background science, from design and synthesis of materials, through materials fabrication issues, to the semiconductor physics of these polymers.

Electroluminescence in conjugated polymers

Charge-Transfer and Energy-Transfer Processes in π-Conjugated Oligomers and Polymers: A Molecular Picture

A review was presented to demonstrate a historical description of the synthesis of light-emitting conjugated polymers for applications in electroluminescent devices. Electroluminescence (EL) was first reported in poly(para-phenylene vinylene) (PPV) in 1990 and researchers continued to make significant efforts to develop conjugated materials as the active units in light-emitting devices (LED) to be used in display applications. Conjugated oligomers were used as luminescent materials and as models for conjugated polymers in the review. Oligomers were used to demonstrate a structure and property relationship to determine a key polymer property or to demonstrate a technique that was to be applied to polymers. The review focused on demonstrating the way polymer structures were made and the way their properties were controlled by intelligent and rational and synthetic design.

Synthesis of Light-Emitting Conjugated Polymers for Applications in Electroluminescent Devices

In recent years, organic solar cells utilizing π-conjugated polymers have attracted widespread interest in both the academic and, increasingly, the commercial communities. These polymers are promising in terms of their electronic properties, low cost, versatility of functionalization, thin film flexibility, and ease of processing. These factors indicate that organic solar cells, although currently producing relatively low power conversion efficiencies (∼5-7%),1–3 compared to inorganic solar cells, have the potential to compete effectively with alternative solar cell technologies. However, in order for this to be feasible, the efficiencies of organic solar cells need further improvement. This is the focus of extensive studies worldwide. The backbone of a π-conjugated polymer is comprised of a linear series of overlapping pz orbitals that have formed via sp2 hybridization, thereby creating a conjugated chain of delocalized electron density. It is the interaction of these π electrons that dictates the electronic characteristics of the polymer. The energy levels become closely spaced as the delocalization length increases, resulting in a ‘band’ structure somewhat similar to that observed in inorganic solid-state semiconductors. In contrast to the latter, however, the primary photoexcitations in conjugated polymers are bound electron-hole pairs (excitons) rather than free charge carriers; this is largely due to their low dielectric constant and the presence of significant electron-lattice interactions and electron correlation effects.4 In the absence of a mechanism to dissociate the excitons into free charge carriers, the exciton will undergo radiative and nonradiative decay, with a typical exciton lifetime in the range from 100 ps to 1 ns. Achieving efficient charge photogeneration has long been recognized as a vital challenge for molecular-based solar cells. For example, the first organic solar cells were simple single-layer devices based on the pristine polymer and two electrodes of different work function. These devices, based on a Schottky diode structure, resulted in poor photocurrent efficiency.5–7 Relatively efficient photocurrent generation in an organic device was first reported by Tang in 1986,8 employing a vacuum-deposited CuPc/ perylene derivative donor/acceptor bilayer device. The differing electron affinities (and/or ionization potentials) between these two materials created an energy offset at their interface, thereby driving exciton dissociation. However, the efficiency of such bilayer devices is limited by the requirement of exciton diffusion to the donor/acceptor interface, typically requiring film thicknesses less than the optical absorption depth. Organic materials usually exhibit exciton diffusion lengths of ∼10 nm and optical absorption depths of 100 nm, although we note significant progress is now being made with organic materials with exciton diffusion lengths comparable to or exceeding their optical absorption depth.9–12 The observation of ultrafast photoinduced electron transfer13,14 from a conjugated polymer to C60 and the * To whom correspondence should be addressed. E-mail: j.durrant@ imperial.ac.uk. Chem. Rev. 2010, 110, 6736–6767 6736

Charge Photogeneration in Organic Solar Cells

Electroluminescence in organic light-emitting diodes arises from a charge-transfer reaction between the injected positive and negative charges by which they combine to form singlet excitons that subsequently decay radiatively. The quantum yield of this process (the number of photons generated per electron or hole injected) is often thought to have a statistical upper limit of 25 per cent. This is based on the assumption that the formation cross-section of singlet excitons, sigmaS, is approximately the same as that of any one of the three equivalent non-radiative triplet exciton states, sigmaT; that is, sigmaS/sigmaT approximately 1. However, recent experimental and theoretical work suggests that sigmaS/sigmaT may be greater than 1. Here we report direct measurements of sigmaS/sigmaT for a large number of pi-conjugated polymers and oligomers. We have found that there exists a strong systematic, but not monotonic, dependence of sigmaS/sigmaT on the optical gap of the organic materials. We present a detailed physical picture of the charge-transfer reaction for correlated pi-electrons, and quantify this process using exact valence bond calculations. The calculated sigmaS/sigmaT reproduces the experimentally observed trend. The calculations also show that the strong dependence of sigmaS/sigmaT on the optical gap is a signature of the discrete excitonic energy spectrum, in which higher energy excitonic levels participate in the charge recombination process.

Formation cross-sections of singlet and triplet excitons in π-conjugated polymers

We report correlated-electron calculations of optically excited states in ten semiconducting single-walled carbon nanotubes with a wide range of diameters Optical excitation occurs to excitons whose binding energies decrease with increasing nanotube diameter, and are smaller than the binding energy of an isolated strand of poly-(paraphenylene vinylene) The ratio of the energy of the second optical exciton polarized along the nanotube axis to that of the lowest exciton is smaller than the value predicted within single-particle theory The experimentally observed weak photoluminescence is an intrinsic feature of semiconducting nanotubes

Electron-electron interaction effects on the optical excitations of semiconducting single-walled carbon nanotubes.

We have studied electronic excited states in films of poly(p-phenylenevinylene) using picosecond transient and cw photomodulation, photoluminescence, and their excitation spectra, as well as electroabsorption spectroscopy. We have determined all the important energy levels of singlet excitons with odd and even parity, the onset of the continuum band, the two-electron (biexciton) states, and the two relevant triplet states, and show that good agreement exists with models involving electron correlation.

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Optical probes of excited states in poly(p-phenylenevinylene).

We investigate multiterminal quantum transport through single monocyclic aromatic annulene molecules, and their derivatives, using the nonequilibrium Green function approach within the self-consistent Hartree-Fock approximation. We propose a new device concept, the quantum interference effect transistor, that exploits perfect destructive interference stemming from molecular symmetry and controls current flow by introducing decoherence and/or elastic scattering that break the symmetry. This approach overcomes the fundamental problems of power dissipation and environmental sensitivity that beset nanoscale device proposals.

Controlling Quantum Transport through a Single Molecule

We show that one-electron band theory fails to describe optical absorption in PPV and the absorption spectrum can be described only within a Coulomb-correlated model. The lowest optical state is an exciton, whose binding energy is estimated theoretically to be 0.90\ifmmode\pm\else\textpm\fi{}0.15 eV. Measurements of the photoconductivity quantum efficiency in poly[2-methoxy,5-(${2}^{\mathcal{'}}$-ethyl-hexyloxy)-1,4 phenylenevinylene] reveal a binding energy in good agreement with the theoretical value.

Sumit Mazumdar

Papers

Formation cross-sections of singlet and triplet excitons in π-conjugated polymers

Electron-electron interaction effects on the optical excitations of semiconducting single-walled carbon nanotubes.

Optical probes of excited states in poly(p-phenylenevinylene).

Controlling Quantum Transport through a Single Molecule

Excitons in poly(para-phenylenevinylene)