Critical wavefunctions in disordered graphene

Vargas, José Eduardo Barrios; Naumis, Gerardo G.

doi:10.1088/0953-8984/24/25/255305

Cited by 9 publications

(28 citation statements)

References 31 publications

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“…Around the Fermi energy, this model presents exponentially localized wavefunctions appear, as has been documented in a previous publication by our group 15 . Such wavefunctions are in agreement with the Abrahams's et.…”

supporting

confidence: 82%

“…scaling analysis, in 1D and 2D all states are localized for any amount of disorder, excluding the possibility of a mobility edge 14 . The experimental and numerical analysis shows that not all states are localized, and there exists a kind of mobility edge associated with a pseudogap around the Fermi energy 9,15,16 . This means that there is a problem that has not been solved.…”

mentioning

confidence: 99%

“…The possibility of having such states has been around in old studies concerning the possibility of having quantum percolation in 2D 19,20 , or in symmetry breaking analysis of graphene 17 . In this case, the extra symmetries of the graphene's lattice makes the problem different from a generic 2D Fermi gas 15 . Such idea has been found by making a random matrix analysis of broken symmetries in the Dirac Hamiltonian when disorder is introduced 17 .…”

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confidence: 99%

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Electron localization in disordered graphene for nanoscale lattice sizes: multifractal properties of the wavefunctions

Vargas

Naumis

2014

2D Mater.

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An analysis of the electron localization properties in doped graphene is performed by doing a numerical multifractal analysis. By obtaining the singularity spectrum of a tight-binding model, it is found that the electron wave functions present a multifractal behavior. Such multifractality is preserved even for second neighbor interaction, which needs to be taken into account if a comparison is desired with experimental results. States close to the Dirac point have a wider multifractal character than those far from this point as the impurity concentration is increased. The analysis of the results allows to conclude that in the split-band limit, where impurities act as vacancies, the system can be well described by a chiral orthogonal symmetry class, with a singularity spectrum transition approaching freezing as disorder increases. This also suggests that in doped graphene, localization is in contrast with the conventional picture of Anderson localization in two dimensions, showing also that the common belief of the absence of quantum percolation in two dimensional systems needs to be revised.Ever since its discovery 1,2 , graphene has been considered as an ideal candidate to replace Silicon in electronics 3 , since this first truly two-dimensional crystal has the highest electrical and thermal conductivity known 4 . However, graphene per se is not a semiconductor. Several proposals have been made to solve this issue 5 . Experimentally, it has been found that doped graphene presents a metal to insulator transition 6 when doped with H, producing a kind of narrow band gap semiconductor. The increase in localization around the Dirac point was roughly predicted from an electron wavefunction frustration analysis in the graphene's underlying triangular lattice 7-9 . Such theoretical results were made under the supposition that Hydrogen bonds to the 2p z Carbon orbital, and thus impurities act as vacancies 10,11 . This case corresponds to the split-band limit. This approach has been useful to predict localization and the pseudogap size, i.e., the region in which the inverse participation ratio increases by one order of magnitude 7 , in very good agreement with experiments 6 , although vacancies and impurities are indeed different 12,13 . However, there is a theoretical nuance to the idea of having a metal-insulator transition in two dimensions (2D). According to the well known Abrahams's et. al. scaling analysis, in 1D and 2D all states are localized for any amount of disorder, excluding the possibility of a mobility edge 14 . The experimental and numerical analysis shows that not all states are localized, and there exists a kind of mobility edge associated with a pseudogap around the Fermi energy 9,15,16 . This means that there is a problem that has not been solved. There are two possibilities, either electron-electron interaction produces delocalization 17 , or somehow the Abrahams's et. al. analysis does not completely applies to this case. In graphene, electron-electron interaction is very weak 18 , so in principle, t...

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confidence: 82%

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confidence: 99%

mentioning

confidence: 99%

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Electron localization in disordered graphene for nanoscale lattice sizes: multifractal properties of the wavefunctions

Vargas

Naumis

2014

2D Mater.

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“…implying that the components of the wavefunction on the A and B sublattices are decoupled. Thus H 2 describes a triangular lattice, and the squaring of H renormalizes one of the bipartite sublattices [45,139] with an spectrum folded around E = 0 that is illustrated in figure 11. As explained before, states near E = 0 need to be close to an antibonding nature in a triangular lattice.…”

Section: Electronic Properties Of Pristine and Disordered Graphenementioning

confidence: 99%

Electronic and optical properties of strained graphene and other strained 2D materials: a review

et al. 2017

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Abstract. This review presents the state of the art in strain and rippleinduced effects on the electronic and optical properties of graphene. It starts by providing the crystallographic description of mechanical deformations, as well as the diffraction pattern for different kinds of representative deformation fields. Then, the focus turns to the unique elastic properties of graphene, and to how strain is produced. Thereafter, various theoretical approaches used to study the electronic properties of strained graphene are examined, discussing the advantages of each. These approaches provide a platform to describe exotic properties, such as a fractal spectrum related with quasicrystals, a mixed DiracSchrödinger behavior, emergent gravity, topological insulator states, in molecular graphene and other 2D discrete lattices. The physical consequences of strain on the optical properties are reviewed next, with a focus on the Raman spectrum. At the same time, recent advances to tune the optical conductivity of graphene by strain engineering are given, which open new paths in device applications. Finally, a brief review of strain effects in multilayered graphene and other promising 2D materials like silicene and materials based on other group-IV elements, phosphorene, dichalcogenide-and monochalcogenide-monolayers is presented, with a brief discussion of interplays among strain, thermal effects, and illumination in the latter material family.

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“…the resulting wave-function is multifractal [47]. In a sample of size L × L, the moments of the participation ratio P q (L) that measures a multifractal localization [48],…”

Section: Folded Deformationsmentioning

confidence: 99%

Energy spectrum for charge carriers in graphene with folded deformations or uniaxial flexural modes: analogies to the quantum Hall effect under random pseudo-magnetic fields

Champo,

Naumis

2021

Preprint

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The electronic behaviour in graphene under a flexural field with random height displacements, considered as pseudo-magnetic fields, is studied. General folded deformations (not necessarily random) were first studied, giving an expression for the zero energy modes. For Gaussian folded deformations, it is possible to use a Coulomb gauge norm for the fields allowing contact with previous work on the quantum Hall effect with random fields, showing that the density of states has a power law behaviour and that the zero energy modes wavefunctions are multifractal. This hints of an unusual electron velocity distribution. Also, an Aharonov-Bohm pseudo-effect is produced. For more general non-folded general flexural strain, is not possible to use a Coulomb gauge. However, a Random Phase Approximation (RPA) and the scheme of random matrix theory allows to tackle the problem. For Gaussian distributed fields, the spectrum presents an average gap and for some cases, a breaking of the particle-hole symmetry. Finally, for the case of Lévy distributed fields, nearly flat bands are seen due to strong electron localization.

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Critical wavefunctions in disordered graphene

Cited by 9 publications

References 31 publications

Electron localization in disordered graphene for nanoscale lattice sizes: multifractal properties of the wavefunctions

Electron localization in disordered graphene for nanoscale lattice sizes: multifractal properties of the wavefunctions

Electronic and optical properties of strained graphene and other strained 2D materials: a review

Energy spectrum for charge carriers in graphene with folded deformations or uniaxial flexural modes: analogies to the quantum Hall effect under random pseudo-magnetic fields

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