Topological Delocalization of Two-Dimensional Massless Dirac Fermions

Nomura, Kentaro; Koshino, Mikito; Ryu, Shinsei

doi:10.1103/physrevlett.99.146806

Cited by 272 publications

(326 citation statements)

References 40 publications

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“…We have demonstrated that the algorithm provides an accuracy and efficiency comparable to the tight-binding model on a honeycomb lattice. In agreement with the existing literature 15,16,17,18 we have found that disorder that is smooth on the scale of the graphene lattice constant enhances conductivity at the Dirac point. The absence of intervalley scattering in the network model may prove useful for the study of these and other single-valley properties.…”

Section: Discussionsupporting

confidence: 92%

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Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model

2008

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The Chalker-Coddington network model (introduced originally as a model for percolation in the quantum Hall effect) is known to map onto the two-dimensional Dirac equation. Here we show how the network model can be used to solve a scattering problem in a weakly doped graphene sheet connected to heavily doped electron reservoirs. We develop a numerical procedure to calculate the scattering matrix with the aide of the network model. For numerical purposes, the advantage of the network model over the honeycomb lattice is that it eliminates intervalley scattering from the outset. We avoid the need to include the heavily doped regions in the network model (which would be computationally expensive), by means of an analytical relation between the transfer matrix through the weakly doped region and the scattering matrix between the electron reservoirs. We test the network algorithm by calculating the conductance of an electrostatically defined quantum point contact and comparing with the tight-binding model of graphene. We further calculate the conductance of a graphene sheet in the presence of disorder in the regime where intervalley scattering is suppressed. We find an increase in conductance that is consistent with previous studies. Unlike the tight-binding model, the network model does not require smooth potentials in order to avoid intervalley scattering.

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Section: Discussionsupporting

confidence: 92%

“…This is consistent with the results obtained in Refs. 15,16,17,18. The effect should not depend on the shape of the tiles in our model for the disorder.…”

Section: Correspondence Between Scattering Matrices Of Dirac Equamentioning

confidence: 91%

Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model

2008

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“…This means that in such samples there exists a minimal non-zero conductivity, which (together with symmetry and spectral flow arguments) led to the conclusion that there is no localization in 1D disordered graphene systems 13,40 . However, this statement (being correct in some sense) should be perceived with a certain caution.…”

Section: Transmission In Disordered Structuresmentioning

confidence: 99%

Transport and localization in periodic and disordered graphene superlattices

et al. 2009

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We study charge transport in one-dimensional graphene superlattices created by applying layered periodic and disordered potentials. It is shown that the transport and spectral properties of such structures are strongly anisotropic. In the direction perpendicular to the layers, the eigenstates in a disordered sample are delocalized for all energies and provide a minimum non-zero conductivity, which cannot be destroyed by disorder, no matter how strong this is. However, along with extended states, there exist discrete sets of angles and energies with exponentially localized eigenfunctions (disorder-induced resonances). Owing to these features, such samples could be used as building blocks in tunable electronic circuits. It is shown that, depending on the type of the unperturbed system, the disorder could either suppress or enhance the transmission. Remarkable properties of the transmission have been found in graphene systems built of alternating p-n and n-p junctions. The mean transmission coefficient has anomalously narrow angular spectrum, practically independent of the amplitude of the fluctuations of the potential. To better understand the physical implications of the results presented here, most of these have been compared with the results for analogous electromagnetic wave systems. Along with similarities, a number of quite surprising differences have been found.

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“…The effect of smooth disorder on transport in graphene has been recently analyzed theoretically by a number of authors, 15,23,24,25,26,27,28 finding once more striking differences with respect to the well known theory of disordered metals. 29 Due to the absence of inter-valley scattering and to chirality conservation, 20 this kind of disorder has the peculiarity of enhancing the conductivity with respect to the ballistic case, which is at odds with classical intuition.…”

Section: Introductionmentioning

confidence: 99%

“…23 suggests the existence of a universal minimal conductivity, whereas recent numerical simulations find that σ increases in a logarithmic fashion with the system size, 24 while the beta function exists (single parameter scaling) and always remains positive. 24,25 One must bear in mind, however, that the conclusions of Ref. 23 rely on a diffusive limit, so that direct comparison to the numerical calculations might not be straightforward.…”

Section: Introductionmentioning

confidence: 99%

Universal scaling of current fluctuations in disordered graphene

San-José

Prada

Golubev³

2007

Phys. Rev. B

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We analyze the full transport statistics of graphene with smooth disorder at low dopings. First we consider the case of one-dimensional (1D) disorder for which the transmission probability distribution is given analytically in terms of the graphene-specific mean free path. All current cumulants are shown to scale with system parameters (doping, size, disorder strength and correlation length) in an identical fashion for large enough systems. In the case of 2D disorder, numerical evidence is given for the same kind of identical scaling of all current cumulants, so that the ratio of any two such cumulants is universal. Specific universal values are given for the Fano factor, which is smaller than the pseudodiffusive value of ballistic graphene (F = 1/3) both for 1D (F ≈ 0.243) and 2D (F ≈ 0.295) disorders. On the other hand, conductivity in wide samples is shown to grow without saturation as √ L and log L with system length L in the 1D and 2D cases respectively.

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Topological Delocalization of Two-Dimensional Massless Dirac Fermions

Cited by 272 publications

References 40 publications

Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model

Calculation of the conductance of a graphene sheet using the Chalker-Coddington network model

Transport and localization in periodic and disordered graphene superlattices

Universal scaling of current fluctuations in disordered graphene

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