Wave transmission and its universal fluctuations in one-dimensional systems with Lévy-like disorder: Schrödinger, Klein-Gordon, and Dirac equations

Barbosa, A. L. R.; Lima, Jonas R.F.; Pereira, Luiz Felipe C.

doi:10.1103/physreve.106.054127

Cited by 4 publications

(3 citation statements)

References 44 publications

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“…Disorder is not the exception in the context of 2D materials. The so-called structural disorder has become a topic of great interest in low dimensional structures based on graphene [21][22][23][24][25][26][27], silicene [28][29][30] and phosphorene [31]. In particular, the transmission and transport properties are affected by the increase of uncorrelated disorder [21,22,28].…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, the tunneling magnetoresistance and valley-spin polarization can be enhanced by the structural disorder [30]. Large-range correlated disorder has been also studied in low-dimensional structures based on 2D materials [23][24][25][26][27]. The long-range correlated disorder associated to the position-dependent velocity of Dirac fermions results in an increase of the conductance when a metallic phase emerges [23].…”

Section: Introductionmentioning

confidence: 99%

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Extended states in random dimer gated graphene superlattices

Rodríguez-González,

García-Cervantes,

García-Rodríguez

et al. 2024

J. Phys.: Condens. Matter

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Ordered and disordered semiconductor superlattices represent structures with completely opposed properties. For instance, ordered superlattices exhibit extended Bloch-like states, while disordered superlattices present localized states. These characteristics lead to higher conductance in ordered superlattices compared to disordered ones. Surprisingly, disordered dimer superlattices, which consist of two types of quantum wells with one type always appearing in pairs, exhibit extended states. The percentage of dissimilar wells does not need to be large to have extended states. Furthermore, the conductance is intermediate between ordered and disordered superlattices. In this work, we explore disordered dimer superlattices in graphene. We calculate the transmission and transport properties using the transfer matrix method and the Landauer-Büttiker formalism, respectively. We identify and discuss the main energy regions where the conductance of random dimer superlattices in graphene is intermediate to that of ordered and disordered superlattices. We also analyze the resonant energies of the double quantum well cavity and the electronic structure of the host gated graphene superlattice, ﬁnding that the coupling between the resonant energies and the superlattice energy minibands gives rise to the extended states in random dimer gated graphene superlattices.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Extended states in random dimer gated graphene superlattices

Rodríguez-González,

García-Cervantes,

García-Rodríguez

et al. 2024

J. Phys.: Condens. Matter

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“…Lévy flights are a particular class of non-Gaussian random walks in which a heavytailed (power-law) distribution describes the step length during the walk [21]. Those flights are present in different fields of science such as the migration pattern of animals [22 and 23], transport in turbulent flows [24], optical wave transport [20,[25][26][27][28][29] and electronic transport [9,[30][31][32][33]. Lévy flights lead to superdiffusive transport, which is characterized by a mean-square displace-ment growing faster than linear with time, i.e., x 2 ∝ t γ , where γ > 1.…”

Section: Introductionmentioning

confidence: 99%

A Lévy flight for electrons in graphene: superdiffusive-to-diffusive transport transition

Fonseca¹,

Pereira²,

Barbosa³

2023

Preprint

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In this work we propose an electronic Lévy flight device, analogous to a recent optical realization. To that end, we investigate the transmission of electrons in graphene nanoribbons in the presence of circular electrostatic clusters, whose diameter follow a power-law distribution. We analyze the effect of the electrostatic clusters on the electronic transport regime of the nanoribbons, in terms of its diffusion behavior. Our numerical calculations show that the presence of circular electrostatic clusters induces a transition from Lévy (superdiffusive) to diffusive transport as the energy increases. Furthermore, we argue that in our electronic Lévy flight device, superdiffusive transport is an exclusive feature of the low-energy quantum regime, while diffusive transport is a feature of the semiclassical regime. Therefore, we attribute the observed transition to the chiral symmetry breaking, once the energy moves away from the Dirac point of graphene.

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