Numerical evidence of spectrum rearrangement in impure graphene

We present a tight-binding theory of the Dirac point resonances due to adsorbed atoms and molecules on an infinite two-dimensional graphene sheet based on the standard tight-binding model of the graphene π -band electronic structure and the extended Hückel model of the adsorbate and nearby graphene carbon atoms. The relaxed atomic geometries of the adsorbates and graphene are calculated using density functional theory. Our model includes the effects of local rehybridization of the graphene from the sp 2 to sp 3 electronic structures that occurs when adsorbed atoms or molecules bond covalently to the graphene. Unlike in previous tight-binding models of Dirac point resonances, adsorbed species with multiple extended molecular orbitals and bonding to more than one graphene carbon atom are treated. More accurate and more general analytic expressions for the Green's function matrix elements that enter the T -matrix theory of Dirac point resonances than have been available previously are obtained. We study H, F, OH, and O adsorbates on graphene and for each we find a strong scattering resonance (two resonances for O) near the Dirac point of graphene, by far the strongest and closest to the Dirac point being the resonance for H. We extract a minimal set of tight-binding parameters that can be used to model resonant electron scattering and electron transport in graphene and graphene nanostructures with adsorbed H, F, OH, and O accurately and efficiently. We also compare our results for the properties of Dirac point resonances due to adsorbates on graphene with those obtained by others using density-functional-theory-based electronic structure calculations and discuss their relative merits. We then present calculations of electronic quantum transport in graphene nanoribbons with these adsorbed species. Our transport calculations capture the physics of the scattering resonances that are induced in the graphene ribbons near the Dirac point by the presence of the adsorbates. We find that the Dirac point resonances play a dominant role in quantum transport in ribbons with adsorbates: Even at low adsorbate concentrations the conductance of the ribbon is strongly suppressed and a transport gap develops for electron Fermi energies near the resonance. The transport gap is centered very near the Dirac point energy for H, below it for F and OH, and above it for O. We find conduction in ribbons with adsorbed H atoms to be very similar to that in ribbons with equal concentrations of carbon atom vacancies. We predict ribbons with adsorbed H, F, OH, and O, under appropriate conditions, to exhibit quantized conductance steps of equal height, similar to those that have been observed by Lin et al. [Phys. Rev. B 78, 161409(R) (2008)] at moderately low temperatures, even for ribbons with conductances a few orders of magnitude smaller than 2e 2 /h.

Section: Introductionmentioning

confidence: 99%

Dirac point resonances due to atoms and molecules adsorbed on graphene and transport gaps and conductance quantization in graphene nanoribbons with covalently bonded adsorbates

Ihnatsenka

Kirczenow

2011

“…When impurity concentration exceeds the critical concentration c r of the spectrum rearrangement, the width of the quasigap starts to increase rapidly with increasing impurity concentration as −2c/ ln c. 17,20,24 Certainly, neither the modified propagator method nor the Kubo expression for the conductivity will work inside this quasigap. Therefore, we will consider only those impurity concentrations that are less than the critical one (c < c r ) in the case of the strong impurity potential.…”

Section: B Strong Scatterersmentioning

confidence: 99%

“…It is not difficult to see that the diagonal element of the Green's function (10) (8) is limited by the scatterings on impurity clusters, 17,20 which contribution to the self-energy will be monitored in what follows.…”

Section: Model Disordered Systemmentioning

confidence: 99%

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Electrical conductivity in graphene with point defects

Skrypnyk

Локтев

2010

The electrical conductivity of graphene containing point defects is studied within the binary alloy model in its dependence on the Fermi level position at the zero temperature. It is found that the minimal conductivity value does not have a universal character and corresponds to the impurity resonance energy rather than to the Dirac point position in the spectrum. The substantial asymmetry of the resulting dependence of the conductivity on the gate voltage magnitude is attributed as well to the very shift of the conductivity minimum to the resonance state energy.

“…The quasiparticle dispersion relation is extracted from the spectral function A(k,E), which can be calculated by extending the well-developed Lanczos approach. 16 In contrast to the previous theoretical studies of the spectral function by the average T-matrix approximation (ATA) [17][18][19] or the selfconsistent T-matrix approximation (SCTA), 17,20 our method is more general and nonperturbative, including all the coherent multiple scattering contributions. We found that, instead of only one peak in the spectral function for a given momentum in the case of a weak short-range scattering, 16 the resonant scattering yields multipeaks in the spectral function.…”

mentioning

confidence: 99%

Vacancy-induced splitting of the Dirac nodal point in graphene

Zhu

Shi

et al. 2012

We investigate the vacancy effects on quasiparticle band structure of graphene near the Dirac point. It is found that each Dirac nodal point splits into two new nodal points due to the coherent multiple scattering among vacancies. The energy split between the two nodal points is proportional to the square root of vacancy concentration. In addition, an extra dispersionless band is developed at zero energy. Our theory offers an excellent explanation to the recent experiments. Electronic properties of materials are often determined by their low-energy excitations. The low-energy excitations of pristine grapheme form the Dirac nodal structures centered at two inequivalent corners K and K of the first Brillouin zone with linear energy dispersion.1,2 The common belief is that the Dirac nodal structure is robust against the shortranged potential scattering because long electron wavelength near the Dirac nodal point would not be able to "see such scatters." 3 However, recent progress in the classical wave physics demonstrates that local resonant structures can dramatically modify waves whose wavelengths are several orders of magnitude larger than the structure sizes. [4][5][6] Vacancies as well as various chemical adsorbates in graphene can create resonant states in the vicinity of the Dirac point. Thus, similar to the classical wave, one expects that electronic structures and transport properties of graphene near the Dirac nodal point can be dramatically modified by vacancies. Indeed, the angleresolved photoemission spectroscopy (ARPES) indicates the opening of a tunable band gap near the Dirac point and the formation of a dispersionless band in hydrogenated quasi-freestanding graphene. 7,8 Another study of hydrogenated graphene on SiC showed signals of a metal-to-insulator transition (MIT) due to the electron localization.9 Away from the charge neutrality point, the transport measurements demonstrated a sublinear carrier dependence of the conductivity.10 Within the Boltzmann transport framework and the assumption of existence of the Dirac nodal structure, theoretical prediction agrees with the experimental observation.11 However, it fails to explain the transport behavior near the nodal point, showing the breakdown of Boltzmann transport theory there. 12,13 In fact, both experiments 7,8 and numerical simulations 14,15 suggest that the Dirac nodal structure is significantly changed by the resonant scattering. Therefore, the discrepancy between the theoretical prediction and transport measurements may arise from the change of quasiparticle behavior near the nodal point, and a deep understanding of the resonant scattering effects is needed.In this Brief Report, we study the effects of the vacancy resonant scattering on Dirac nodal structure in graphene. The quasiparticle dispersion relation is extracted from the spectral function A(k,E), which can be calculated by extending the well-developed Lanczos approach. 16 In contrast to the previous theoretical studies of the spectral function by the average T-matrix approximatio...