Evaluation of the Green’s function of disordered graphene

Zhu, Wei; Shi, Qinwei; Wang, X. R.; Wang, X. P.; Yang, Lu; Chen, J.; Hou, J. G.

doi:10.1103/physrevb.82.153405

Cited by 19 publications

(19 citation statements)

References 48 publications

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“…These general features are indeed observed in the weak point potential scattering cases. 16 The spectral function is qualitatively different in the strongly resonant scattering regime. Taking A(k = 0+, E) in Fig.…”

Section: Self-energy Function Is Defined By the Dyson's Equation As Gmentioning

confidence: 99%

“…2(b) and 2(c). 16 Away from the Dirac point, the p + peak dominates the spectral function and the effective energy dispersion approaches the linear behavior (red square dotted line). Around the Dirac point, Fig.…”

Section: Self-energy Function Is Defined By the Dyson's Equation As Gmentioning

confidence: 99%

“…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.…”

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confidence: 99%

“…This Green function can be obtained numerically by using the Lanczos recursive method. 15,16,[23][24][25] To numerically obtain an exact ensemble-averaged Green's function near the Dirac point, a large lattice containing millions sites (4800 × 4800) is used. The large samples guarantee that the calculated Green's function is free from the finite size errors.…”

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confidence: 99%

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Vacancy-induced splitting of the Dirac nodal point in graphene

Zhu

Shi

et al. 2012

Phys. Rev. B

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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...

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Section: Self-energy Function Is Defined By the Dyson's Equation As Gmentioning

confidence: 99%

Section: Self-energy Function Is Defined By the Dyson's Equation As Gmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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Vacancy-induced splitting of the Dirac nodal point in graphene

Zhu

Shi

et al. 2012

Phys. Rev. B

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“…24 The DOS can also be obtained by averaging over all LDOS's and/or through an ensemble average. In this approach, a small artificial cutoff energy = 1 meV is introduced to simulate the infinitesimal imaginary energy ν, 31,32 which will lead to a small width of LL's in clean graphene. To reduce the finite-size effects, a very large lattice of more than one million sites (N > 10 6 ) is used.…”

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Shape of the Landau subbands in disordered graphene

et al. 2011

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The question of why different experiments obtain different shapes of Landau subbands of two-dimensional electron gases (2DEG's) is investigated. In particular, we consider disordered graphene within the tight-binding formulation in a high magnetic field and in the presence of impurity potentials of a finite interaction range. It is found that the shape of the total density of states (DOS) of Landau subbands is well described by a Gaussian function, while the shape of the local density of states (LDOS) can be fitted to either a simple Lorentzian function or a sum of several Lorentzian functions. This finding explains well why the experiments that measure the DOS of a Landau subband appear to be Gaussian, and those experiments that are sensitive to the LDOS can only be fitted well by Lorentzian functions. Thus, our results provide a natural explanation to this long-standing puzzle involving 2DEG's in the quantum Hall regime. Graphene has attracted a lot of attention due to its remarkable properties and its potential applications in nanoelectronics. 1 Its electronic properties are mainly due to its two-dimensional nature and the fact that the low-energy excitations are governed by the massless Dirac equation, 2 confirmed by the interesting, uneven Landau level (LL) distribution that varies with both the square root of the magnetic field B and the LL index n: E n = sgn(n) 2ehv 2 F |n|B, where v F , e, andh are the Fermi velocity, electron charge, and the Planck constant, respectively. This emblematic LL spectrum and its characteristic zero-energy state (n = 0) are directly related to the anomalous quantum Hall effect (QHE) in graphene. 3 Many efforts have been made to determine the electronic properties of the disorder-broadened Landau subbands (LS's). However, the shape of both the total density of states (DOS) and the local DOS (LDOS) of an LS of graphene is a controversial issue in the literature. Historically, it has generally been believed that the shape of the DOS of LS's in a conventional two-dimensional electron gas (2DEG) is Gaussian-like, 4,5 but experiments seem to present a different picture. Initially, this consensus was supported by careful measurements of specific heat, 6 magnetization, 7 and magnetocapacitance 8 on GaAs-Ga x Al 1−x As heterostructures. However, a recent scanning-tunneling-microscopy-scanningtunneling-spectroscopy (STM-STS) measurement on conventional 2DEG's of the n-InSb(110) ] surface, 9 as well as the cyclotron resonance (CR) absorption line shape on conventional 2DEG's, 10,11 observed a Lorentzian shape of an LS. The situation for disordered graphene is similar. All CR 13-15 and STM-STS 16-19 measurements suggested clearly a Lorentzian shape for an LS. However, recent magnetocapacitance experiments produced conflicting results: In one experiment, 20 an LS could be fitted well by the Lorentzian functions, while another experiment 21 observed a Gaussian shape for an n = 0 LS. On the theoretical side, the DOS of an LS of graphene is initially found to be Gaussian-like. [22][23][24] C...

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Electronic structure of disordered graphene with Greenʼs function approach

2012

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The Green functions play a big role in the calculation of the local density of states of the carbon nanostructures. We investigate their nature for the variously oriented and disclinated graphene-like surface. Next, we investigate the case of a small perturbation generated by two heptagonal defects and from the character of the local density of states in the border sites of these defects we derive their minimal and maximal distance on the perturbed cylindrical surface. For this purpose, we transform the given surface into a chain using the Haydock recursion method. We will suppose only the nearest-neighbor interactions between the atom orbitals, in other words, the calculations suppose the short-range potential.

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Evaluation of the Green’s function of disordered graphene

Cited by 19 publications

References 48 publications

Vacancy-induced splitting of the Dirac nodal point in graphene

Vacancy-induced splitting of the Dirac nodal point in graphene

Shape of the Landau subbands in disordered graphene

Electronic structure of disordered graphene with Greenʼs function approach

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