Fluctuation phenomena in chaotic Dirac quantum dots: Artificial atoms on graphene flakes

Ramos, J. Galvão; Hussein, M. S.; Barbosa, A. L. R.

doi:10.1103/physrevb.93.125136

Cited by 17 publications

(8 citation statements)

References 59 publications

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“…In RQC, topics that have been studied so far include energy level-spacing statistics in graphene systems [115][116][117][118][119][120], relativistic quantum scarring [121][122][123][124], relativistic quantum chaotic scattering and transport [125][126][127][128][129][130][131][132][133], quantum resonant tunneling in Dirac fermion and graphene systems [134][135][136], effects of chaos and random disorder on persistent currents in Dirac fermion sys-tems [137][138][139], the role of classical dynamics in confinement of massless Dirac fermions [140][141][142][143], chaos and spin transport in graphene quantum dot systems [144], and the interplay among chaos, relativistic quantum mechanics, and many body interaction in graphene billiards [136,145].…”

Section: What Has Been Done In Rqc?mentioning

confidence: 99%

“…In general, the boundaries of a closed graphene domain will mix the quantum dynamics associated with the two valleys, implying that the two-component Dirac equation cannot provide a completely accurate description of graphene systems. Nevertheless, analysis and solutions of the 2D Dirac equation in an arbitrary geometrical shape can provide insights into the behaviors of the graphene billiard of the same shape and understanding of phenomena such as chaotic scattering [132,140,141,201].…”

Section: Boundary Conditions For Graphene Billiardsmentioning

confidence: 99%

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Relativistic quantum chaos

Huang

Grebogi

et al. 2018

Physics Reports

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Quantum chaos is generally referred to as the study of quantum manifestations or fingerprints of nonlinear dynamical and chaotic behaviors in the corresponding classical system, an interdisciplinary field that has been active for about four decades. In closed chaotic Hamiltonian systems, for example, the basic phenomena studied include energy level-spacing statistics and quantum scarring. In open Hamiltonian systems, quantum chaotic scattering has been investigated extensively. Previous works were almost exclusively for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid growth of interest in Dirac materials such as graphene, topological insulators, molybdenum disulfide and topological Dirac semimetals. A common feature of these materials is that their physics is described by the Dirac equation in relativistic quantum mechanics, generating phenomena that do not usually emerge in conventional semiconductor materials. This has important consequences. In particular, at the level of basic science, a new field has emerged: Relativistic Quantum Chaos (RQC), which aims to uncover, understand, and exploit relativistic quantum manifestations of classical nonlinear dynamical behaviors including chaos. Practically, Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, and have led to novel device concepts such as valleytronics. Exploiting manifestations of nonlinear dynamics and chaos in the relativistic quantum regime can have significant applications.The aim of this article is to give a comprehensive review of the basic results obtained so far in the emergent field of RQC. Phenomena to be discussed in depth include energy level-spacing statistics in graphene or Dirac fermion systems that exhibit various nonlinear dynamical behaviors in the classical limit, relativistic quantum scars (unusually high concentrations of relativistic quantum spinors about classical periodic orbits), peculiar features of relativistic quantum chaotic scattering and quantum transport, manifestations of the Klein paradox and its effects on graphene or 2D Dirac material based devices, chaos based modulation of conductance fluctuations in relativistic quantum dots, regularization of relativistic quantum tunneling by chaos, superpersistent currents in chaotic Dirac rings subject to a magnetic flux, and exploitation of relativistic quantum whispering gallery modes for applications in quantum information science. Computational methods for solving the Dirac equation in various situations will be introduced and physical theories developed so far in RQC will be described. Potential device applications will be discussed.

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Section: What Has Been Done In Rqc?mentioning

confidence: 99%

Section: Boundary Conditions For Graphene Billiardsmentioning

confidence: 99%

Relativistic quantum chaos

Huang

Grebogi

et al. 2018

Physics Reports

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“…At the level of basic science, a new field has emerged: Relativistic Quantum Chaos (RQC), which aims to uncover, understand, and exploit relativistic quantum manifestations of classical nonlinear dynamical behaviors including chaos. Topics studied so far include relativistic quantum scarring, 121,134,136,153 energy level spacing statistics in graphene systems, 123,[125][126][127]130 relativistic quantum chaotic scattering and transport, 128,131,139,142,145,149,150,154 relativistic quantum tunneling, 133,141,143 effects of chaos on persistent currents in Dirac fermion systems, 146,148 the role of classical dynamics in confinement of massless Dirac fermions, 122,129,135,144 the interplay between chaos and spin transport in graphene quantum dot systems, 151 and the role of many body interactions in chaotic graphene quantum billiards. 143,152 From an applied point of view, due to the underlying physics being effectively governed by the Dirac equation, purely relativistic quantum phenomena such as Klein tunneling, Zitterbewegung, and pair creations can potentially occur in solid state devices and be exploited for significantly improving or even revolutionizing conventional electronics and spintronics.…”

Section: Introductionmentioning

confidence: 99%

Relativistic quantum chaos—An emergent interdisciplinary field

Lai

Huang

et al. 2018

Chaos: An Interdisciplinary Journal of Nonlinear Science

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Quantum chaos is referred to as the study of quantum manifestations or fingerprints of classical chaos. A vast majority of the studies were for nonrelativistic quantum systems described by the Schrödinger equation. Recent years have witnessed a rapid development of Dirac materials such as graphene and topological insulators, which are described by the Dirac equation in relativistic quantum mechanics. A new field has thus emerged: relativistic quantum chaos. This Tutorial aims to introduce this field to the scientific community. Topics covered include scarring, chaotic scattering and transport, chaos regularized resonant tunneling, superpersistent currents, and energy level statistics-all in the relativistic quantum regime. As Dirac materials have the potential to revolutionize solid-state electronic and spintronic devices, a good understanding of the interplay between chaos and relativistic quantum mechanics may lead to novel design principles and methodologies to enhance device performance.

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“…More applications of these kind of ideas in mesoscopic transport in quantum dots can be found in Refs. [24][25][26].…”

Section: Further Developmentsmentioning

confidence: 99%