Transport and localization in periodic and disordered graphene superlattices

Bliokh, Yu. P.; Freilikher, V.; Savel’ev, Sergey; Nori, Franco

doi:10.1103/physrevb.79.075123

Cited by 104 publications

(106 citation statements)

References 53 publications

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“…In a related work, 55 localization of Dirac particles in 1D disordered potentials was studied, but only for zero incidence angle θ (i.e., wave vector of charge carriers normal to the interface between different GSL layers) and without analytical results for the localization length. Another closely related theoretical study of disordered GSLs 56 comprised an analytical discussion of the scattering transmission only for sufficiently small θ and random barrier heights. Our work extends all previous results, to the best of our knowledge, inasmuch as it covers the analytical properties of the localization length for all values of θ, for different types of disorder, and for both scalar and vector GSLs.…”

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confidence: 99%

Localization behavior of Dirac particles in disordered graphene superlattices

2012

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Graphene superlattices (GSLs), formed by subjecting a monolayer graphene sheet to a periodic potential, can be used to engineer band structures and, from there, charge transport properties, but these are sensitive to the presence of disorder. The localization behavior of massless 2D Dirac particles induced by weak disorder is studied for both scalar-potential and vector-potential GSLs, computationally as well as analytically by a weak-disorder expansion. In particular, it is investigated how the Lyapunov exponent (inverse localization length) depends on the incidence angle to a 1D GSL. Delocalization resonances are found for both scalar and vector GSLs. The sharp angular dependence of the Lyapunov exponent may be exploited to realize disorder-induced filtering, as verified by full 2D numerical wave packet simulations.

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confidence: 99%

Localization behavior of Dirac particles in disordered graphene superlattices

2012

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“…Motivated by the experimental realization of graphene superlattice (GSL) [10][11][12], electronic bandgap structures and transport properties in GSLs with electrostatic potential and magnetic barrier have been extensively investigated [13][14][15][16][17][18][19][20][21][22], since the conventional semiconductor superlattices are successful in controlling the electronic structures and the extension to graphene may give rise to different features and applications. For instance, DP appears in the GSL [14,15], and it is exactly located at the energy with the zero-k gap [17].…”

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confidence: 99%

“…As we know, the quasi-periodic GSL is classified as intermediate between ordered and disordered systems [19,20], which has significant and common features like fractal spectrum and self-similar behavior [21,22]. How- * Corresponding author.…”

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confidence: 99%

Electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice

Zhao

Chen

2011

Applied Physics Letters

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We investigate electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice. It is found that such structure can possess a zero-k gap which exists in all Fibonacci sequences. Different from Bragg gap, zero-k gap associated with Dirac point is less sensitive to the incidence angle and lattice constants. The defect mode appeared inside the zero-k gap has a great effect on transmission, conductance and shot noise, which can be applicable to control the electron transport.Graphene, a monolayer of carbon atoms tightly packed into a honeycomb lattice, has attracted great interest in graphene-based nanoelectronic and optoelectronic devices [1], since it was fabricated by Novoselov and Geim et al. in 2004 [2]. In graphene, the unique band structure with the valance and conduction bands touching at Dirac point (DP) leads to the fact that electrons around the Fermi level can be described as the massless relativistic Dirac electrons, resulting in the linear energy dispersion relation. As a consequence, there are a great number of electronic properties, such as the half-integer quantum Hall effect [3][4][5], the minimum conductivity [3], and Klein tunneling [6]. In particular, Klein tunneling and perfect transmission are crucial for electron transport in various graphene heterostructures [7], i.e. single barrier [8] and n-p-n junctions [9].Motivated by the experimental realization of graphene superlattice (GSL) [10][11][12], electronic bandgap structures and transport properties in GSLs with electrostatic potential and magnetic barrier have been extensively investigated [13][14][15][16][17][18][19][20][21][22], since the conventional semiconductor superlattices are successful in controlling the electronic structures and the extension to graphene may give rise to different features and applications. For instance, DP appears in the GSL [14,15], and it is exactly located at the energy with the zero-k gap [17]. Interestingly, the zero-k gap associated with DP is insensitive to the lattice parameter changes in contrast with the behavior exhibited by Bragg gaps [17]. This gap is analogous to photonic zero-n gap in the photonic crystals containing negativeindex and positive-index materials [20], and originates from a zero total phase [23]. Accordingly, the zero-k gap is robust against the lattice constants, structural disorder [17], and external magnetic field [18], and thus is better to control the electron transport in GSL.In this Letter, we will investigate electronic band gap and transport in Fibonacci quasi-periodic GSLs in the fashion analogous to photonic crystal with metamaterials [23][24][25]. As we know, the quasi-periodic GSL is classified as intermediate between ordered and disordered systems [19,20], which has significant and common features like fractal spectrum and self-similar behavior [21,22]. How- * Corresponding author. Email: xchen@shu.edu.cn ever, what we concentrate on here is the electronic band gap and DP in such quasi-periodic system. We find that zero-k gap happens in all Fibonacci...

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“…Historically, the analogy between Maxwell equations and those used in the relativistic electron theory has been discussed in different contexts and for various purposes (see, for example, 47,[92][93][94] ) since 1907 when Maxwell equations were reduced 95 to an alternative, more concise form by introducing a complex field F = E + iH:…”

Section: B Charge Transport In Disordered Graphenementioning

confidence: 99%

“…In Section IV B, conducting properties of a graphene layer subject to stratified electric field are considered. The close analogy between charge transport in such system and wave transmission through multilayered stack 47 underpins remarkable conductive properties of disordered graphene 48 . We predict disorder-induced resonances of the transmission coefficient at oblique incidence of electron waves.…”

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confidence: 94%

Anderson localization in metamaterials and other complex media (Review Article)

Gredeskul

Kivshar

Asatryan

et al. 2012

Low Temperature Physics

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We review some recent (mostly ours) results on the Anderson localization of light and electron waves in complex disordered systems, including: (i) left-handed metamaterials, (ii) magneto-active optical structures, (iii) graphene superlattices, and (iv) nonlinear dielectric media. First, we demonstrate that left-handed metamaterials can significantly suppress localization of light and lead to an anomalously enhanced transmission. This suppression is essential at the long-wavelength limit in the case of normal incidence, at specific angles of oblique incidence (Brewster anomaly), and in the vicinity of the zero-ε or zero-µ frequencies for dispersive metamaterials. Remarkably, in disordered samples comprised of alternating normal and left-handed metamaterials, the reciprocal Lyapunov exponent and reciprocal transmittance increment can differ from each other. Second, we study magneto-active multilayered structures, which exhibit nonreciprocal localization of light depending on the direction of propagation and on the polarization. At resonant frequencies or realizations, such nonreciprocity results in effectively unidirectional transport of light. Third, we discuss the analogy between the wave propagation through multilayered samples with metamaterials and the charge transport in graphene, which enables a simple physical explanation of unusual conductive properties of disordered graphene superlatices. We predict disorder-induced resonances of the transmission coefficient at oblique incidence of the Dirac quasiparticles. Finally, we demonstrate that an interplay of nonlinearity and disorder in dielectric media can lead to bistability of individual localized states excited inside the medium at resonant frequencies. This results in nonreciprocity of the wave transmission and unidirectional transport of light.

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Transport and localization in periodic and disordered graphene superlattices

Cited by 104 publications

References 53 publications

Localization behavior of Dirac particles in disordered graphene superlattices

Localization behavior of Dirac particles in disordered graphene superlattices

Electronic band gap and transport in Fibonacci quasi-periodic graphene superlattice

Anderson localization in metamaterials and other complex media (Review Article)

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