Density of States in Graphene with Vacancies: Midgap Power Law and Frozen Multifractality

We demonstrate that a nonzero concentration n v of static, randomly placed vacancies in graphene leads to a density w of zero-energy quasiparticle states at the band center ϵ ¼ 0 within a tight-binding description with nearest-neighbor hopping t on the honeycomb lattice. We show that w remains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder and depends sensitively on n v and correlations between vacancy positions. For low, but not-too-low, jϵj=t in this compensated case, we show that the density of states ρðϵÞ exhibits a strong divergence of the form ρ Dyson ðϵÞ ∼ jϵj −1 =½logðt=jϵjÞ ðyþ1Þ , which crosses over to the universal low-energy asymptotic form (modified Gade-Wegner scaling) expected on symmetry grounds ρ GW ðϵÞ ∼ jϵj −1 e −b½logðt=jϵjÞ 2=3 below a crossover scale ϵ c ≪ t. ϵ c is found to decrease rapidly with decreasing n v , while y decreases much more slowly. DOI: 10.1103/PhysRevLett.117.116806 Static impurities, which give rise to random timeindependent terms in the single-particle Hamiltonian for quasiparticle excitations of a condensed matter system, can lead to the phenomenon of Anderson localization, whereby quasiparticle wave functions lose their plane-wave character and become localized [1]. Such localization transitions and universal low-energy properties of the localized phase have been successfully described in many cases using effective field theories [2,3] whose form depends on symmetry properties of the quasiparticle Hamiltonian in the presence of impurities. In some cases [4,5], it has also been possible to refine these field-theoretical predictions using real-space strong-disorder renormalization group ideas [6].In this Letter, we study the effects of a nonzero concentration n v of static, randomly located vacancies in graphene. We use a tight-binding description for electronic states of graphene, with hopping amplitude t between nearest-neighbor sites on a honeycomb lattice, and model vacancies by the deletion of the corresponding site in this tight-binding model [7][8][9][10][11]. We focus on the compensated case, i.e., exactly equal numbers of vacancies on the two sublattices of the honeycomb lattice, and demonstrate that vacancies generically lead to a nonuniversal density w of zero-energy quasiparticle states at the band center ϵ ¼ 0 even in this compensated case, including in the presence of hopping disorder. For low, but not-too-low, jϵj=t in this compensated case, the density of states (DOS) ρðϵÞ exhibits a strong divergence of the formfamiliar in the context of various random-hopping problems in one dimension [12][13][14][15][16][17][18][19][20]. At still lower energies, below a crossover scale ϵ c that is several orders of magnitude smaller than t even for moderately small values of n v (0.05-0.1), we show that the DOS crosses over to the low-energy asymptotic behavior [4-6,21] of the chiral orthogonal universality class (to which our tight-binding model belongs on symmetry grou...

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“…(2)] expected on symmetry grounds. In parallel work [24], this prediction was found to be consistent with numerical results for the DOS.…”

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confidence: 75%

Vacancy-Induced Low-Energy States in Undoped Graphene

2016

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“…The vanishing of the β function of the effective nonlinear sigma model (NLσM) led Ostrovsky et al to conjecture a line of fixed points with nonuniversal metallic conductivity of the order of the conductance quantum σð0Þ ≈ e 2 =h [22][23][24]. However, the validity of the NLσM of the BDI class has been questioned, as vacancies are infinitely strong scatterers, not amenable to perturbative analysis [12]. On the other hand, numerical evaluations of the conductivity using wave-packet propagation methods show localization of all states σðEÞ → 0, including the ZEMs [19][20][21].…”

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confidence: 99%

“…On the other hand, numerical evaluations of the conductivity using wave-packet propagation methods show localization of all states σðEÞ → 0, including the ZEMs [19][20][21]. The Gade singularity in the DOS approaching E → 0 [12], however, raises questions on the validity of the extraction of the conductivity using wave-packet propagation methods.…”

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confidence: 99%

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Critical Delocalization of Chiral Zero Energy Modes in Graphene

2015

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Graphene subjected to chiral-symmetric disorder is believed to host zero energy modes (ZEMs) resilient to localization, as suggested by the renormalization group analysis of the underlying nonlinear sigma model. We report accurate quantum transport calculations in honeycomb lattices with in excess of 10 9 sites and fine meV resolutions. The Kubo dc conductivity of ZEMs induced by vacancy defects (chiral BDI class) is found to match 4e 2 =πh within 1% accuracy, over a parametrically wide window of energy level broadenings and vacancy concentrations. Our results disclose an unprecedentedly robust metallic regime in graphene, providing strong evidence that the early field-theoretical picture for the BDI class is valid well beyond its controlled weak-coupling regime.

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“…The latter are predicted to introduce power-law localized midgap states at the Dirac point [26][27][28], displaying anomalous divergent behavior of the density of states [29,30]. These so-called resonant scatterers have a profound impact on charge carrier transport at all carrier densities, invalidating conventional transport pictures based on the weak disorder hypothesis [31][32][33].…”

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confidence: 94%

Electrically tunable resonant scattering in fluorinated bilayer graphene

Stabile

Ferreira

et al. 2015

Phys. Rev. B

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Adatom-decorated graphene offers a promising new path towards spintronics in the ultrathin limit. We combine experiment and theory to investigate the electronic properties of dilutely fluorinated bilayer graphene, where the fluorine adatoms covalently bond to the top graphene layer. We show that fluorine adatoms give rise to resonant impurity states near the charge neutrality point of the bilayer, leading to strong scattering of charge carriers and hopping conduction inside a field-induced band gap. Remarkably, the application of an electric field across the layers is shown to tune the resonant scattering amplitude from fluorine adatoms by nearly twofold. The experimental observations are well explained by a theoretical analysis combining Boltzmann transport equations and fully quantum-mechanical methods. This paradigm can be generalized to many bilayer graphene-adatom materials, and we envision that the realization of electrically tunable resonance may be a key advantage in graphene-based spintronic devices.Comment: pdflatex, 18 pages including supplementary materials, 4 figures in the main text, 5 figures in the supplementary materia

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Density of States in Graphene with Vacancies: Midgap Power Law and Frozen Multifractality

Cited by 42 publications

References 35 publications

Vacancy-Induced Low-Energy States in Undoped Graphene

Vacancy-Induced Low-Energy States in Undoped Graphene

Critical Delocalization of Chiral Zero Energy Modes in Graphene

Electrically tunable resonant scattering in fluorinated bilayer graphene

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