The two dimensional Hubbard model: a theoretical tool for molecular electronics (original) (raw)
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Physical Review B, 2011
An efficient computational methodology is used to explore charge transport properties in chemically modified (and randomly disordered) graphene-based materials. The Hamiltonians of various complex forms of graphene are constructed using tight-binding models enriched by first-principles calculations. These atomistic models are further implemented into a real-space order-N Kubo-Greenwood approach, giving access to the main transport length scales (mean free paths, localization lengths) as a function of defect density and charge carrier energy. An extensive investigation is performed for epoxide impurities with specific discussions on both the existence of a minimum semiclassical conductivity and a crossover between weak to strong localization regime. The 2D generalization of the Thouless relationship linking transport length scales is here illustrated based on a realistic disorder model.
AC conductivity of graphene: From tight-binding model to 2 + 1-dimensional quantum electrodynamics
2007
We consider the relationship between the tight-binding Hamiltonian of the twodimensional honeycomb lattice of carbon atoms with nearest neighbor hopping only and the 2 + 1 dimensional Hamiltonian of quantum electrodynamics which follows in the continuum limit. We pay particular attention to the symmetries of the free Dirac fermions including spatial inversion, time reversal, charge conjugation and chirality. We illustrate the power of such a mapping by considering the effect of the possible symmetry breaking which corresponds to the creation of a finite Dirac mass, on various optical properties. In particular, we consider the diagonal AC conductivity with emphasis on how the finite Dirac mass might manifest itself in experiment. The optical sum rules for the diagonal and Hall conductivities are discussed.
Electronic transport in two dimensional graphene
2010
We provide a broad review of fundamental electronic properties of two-dimensional graphene with the emphasis on density and temperature dependent carrier transport in doped or gated graphene structures. A salient feature of our review is a critical comparison between carrier transport in graphene and in two-dimensional semiconductor systems (e.g. heterostructures, quantum wells, inversion layers) so that the unique features of graphene electronic properties arising from its gap- less, massless, chiral Dirac spectrum are highlighted. Experiment and theory as well as quantum and semi-classical transport are discussed in a synergistic manner in order to provide a unified and comprehensive perspective. Although the emphasis of the review is on those aspects of graphene transport where reasonable consensus exists in the literature, open questions are discussed as well. Various physical mechanisms controlling transport are described in depth including long- range charged impurity scattering, screening, short-range defect scattering, phonon scattering, many-body effects, Klein tunneling, minimum conductivity at the Dirac point, electron-hole puddle formation, p-n junctions, localization, percolation, quantum-classical crossover, midgap states, quantum Hall effects, and other phenomena.
The Journal of Chemical Physics, 2009
It is shown that, within the tight-binding approximation, Fermi-level ballistic conduction for a perimeter-connected graphene fragment follows a simple selection rule: the zero eigenvalues of the molecular graph and of its subgraph minus both contact vertices must be equal in number, as must those of the two subgraphs with single contact vertices deleted. In chemical terms, the new rule therefore involves counting nonbonding orbitals of four molecules. The rule is initially derived within the source and sink potential scattering framework, but has equivalent forms that unify the molecular-orbital and valence-bond approaches to conduction. It is shown that the new selection rule can be cast in terms of Kekulé counts, bond orders, and frontier-orbital coefficients. In particular, for a Kekulean graphene, conduction pathways are shown to be ranked in efficiency by a ͑nonmonotonic͒ function of Pauling bond order between the contact vertices. Frontier-orbital analysis of conduction approximates this function. For a monoradical graphene, the analogous function is shown to depend on Pauling spin densities at contact vertices.
Some "Exotic" Conductivity Mechanisms in Graphene
In the fractal approximation of movement, some conductivity mechanisms in graphene are analyzed. So, using a field theory with spontaneous symmetry breaking the integer quantum Hall effect is obtained while, through a two-dimensional nonlinear Toda-lattice method, the fractional quantum Hall effect results. These two effects can explain the electrical conductivities in graphene.
Physical Review B, 1975
The recent theoretical work on the one-dimensional Hubbard model showed this to be inadequate to explain the properties of n-methyl phenazinium tetracyanoquino dimethane (NMP-TCNQ) in the regime of narrow bandwidth compared to Coulomb repulsion; however, it also supported the suggestion existing in the literature that it is possible to fit both the magnetic susceptibility and the low-T activation energy of the electrical conductivity by introducing a temperature dependence in the parameters of the Hamiltonian. Since the Hubbard Hamiltonian neglects important interactions (long-range Coulomb repulsion, electron-lattice interaction, etc.), it is reasonable to think that these interactions may be responsible for this temperature dependence. In this paper I add to the Hubbard Hamiltonian a nearest-neighbor Coulomb interaction and calculate the electrical conductivity in the narrow-bandwidth regime.
Exact Results for Intrinsic Electronic Transport in Graphene
Chinese Physics Letters, 2012
We present exact results for the electronic transport properties of graphene sheets connected to two metallic electrodes. Our results, obtained by transfer-matrix methods, are valid for all sheet widths and lengths. In the limit of large width-to-length ratio relevant to recent experiments, we find a Dirac-point conductivity of 2e 2 / √ 3h and a sub-Poissonian Fano factor of 2 − 3 √ 3/π ≃ 0.346 for armchair graphene; for the zigzag geometry these are respectively 0 and 1. Our results reflect essential effects from both the topology of graphene and the electronic structure of the leads, giving a complete microscopic understanding of the unique intrinsic transport in graphene. PACS numbers: 72.80.Vp, 73.22.Pr,73.40.Sx Graphene, a graphite monolayer of carbon atoms forming a honeycomb lattice, has a distinctive electronic structure whose low energy excitations are described by massless Dirac fermions. The successful extraction of micron-scale graphene sheets from a natural graphite crystal, and their deposition onto an oxidized Si wafer [1], was a truly seminal event which ushered in a new era of realistic experimental and theoretical exploration. The subsequent explosion of graphene activity has focused on fundamental questions concerning the transport properties of relativistic particles in graphene and on its potential applications as a high-mobility semiconductor.
Electronic properties of disordered two-dimensional carbon
Physical Review B, 2006
Two-dimensional carbon, or graphene, is a semi-metal that presents unusual low-energy electronic excitations described in terms of Dirac fermions. We analyze in a self-consistent way the effects of localized (impurities or vacancies) and extended (edges or grain boundaries) defects on the electronic and transport properties of graphene. On the one hand, point defects induce a finite elastic lifetime at low energies with the enhancement of the electronic density of states close to the Fermi level. Localized disorder leads to a universal, disorder independent, electrical conductivity at low temperatures, of the order of the quantum of conductance. The static conductivity increases with temperature and shows oscillations in the presence of a magnetic field. The graphene magnetic susceptibility is temperature dependent (unlike an ordinary metal) and also increases with the amount of defects. Optical transport properties are also calculated in detail. On the other hand, extended defects induce localized states near the Fermi level. In the absence of electron-hole symmetry, these states lead to a transfer of charge between the defects and the bulk, the phenomenon we call selfdoping. The role of electron-electron interactions in controlling self-doping is also analyzed. We also discuss the integer and fractional quantum Hall effect in graphene, the role played by the edge states induced by a magnetic field, and their relation to the almost field independent surface states induced at boundaries. The possibility of magnetism in graphene, in the presence of short-range electron-electron interactions and disorder is also analyzed.