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      Nonstandard transition GUE-GOE for random matrices and spectral statistics of graphene nanoflakes

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          Abstract

          Spectral statistics of weakly-disordered triangular graphene flakes with zigzag edges are revisited. Earlier, we have found numerically that such systems may shown spectral fluctuations of GUE, signalling the time-reversal symmetry breaking at zero magnetic field, accompanied by approximate twofold valley degeneracy of each energy level [Phys. Rev. B 85, 245424 (2012)]. Atomic-scale disorder induce the scattering of charge carriers between the valleys and restores the spectral fluctuations of GOE. A simplified description of such a nonstandard GUE-GOE transition, employing the mixed ensemble of 4x4 real symmetric matrices was also proposed. Here we complement our previous study by analyzing numerically the spectral fluctuations of large matrices belonging the same mixed ensemble. Resulting scaling laws relate the ensemble parameter to physical size and the number of atomic-scale defects in graphene flake. A phase diagram, indicating the regions in which the signatures of GUE may by observable in the size-doping parameter plane, is presented.

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          Most cited references18

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          Graphene: Status and Prospects

          A. K. Geim (2010)
          Graphene is a wonder material with many superlatives to its name. It is the thinnest material in the universe and the strongest ever measured. Its charge carriers exhibit giant intrinsic mobility, have the smallest effective mass (it is zero) and can travel micrometer-long distances without scattering at room temperature. Graphene can sustain current densities 6 orders higher than copper, shows record thermal conductivity and stiffness, is impermeable to gases and reconciles such conflicting qualities as brittleness and ductility. Electron transport in graphene is described by a Dirac-like equation, which allows the investigation of relativistic quantum phenomena in a bench-top experiment. What are other surprises that graphene keeps in store for us? This review analyses recent trends in graphene research and applications, and attempts to identify future directions in which the field is likely to develop.
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            Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells

            We show that the Quantum Spin Hall Effect, a state of matter with topological properties distinct from conventional insulators, can be realized in HgTe/CdTe semiconductor quantum wells. By varying the thickness of the quantum well, the electronic state changes from a normal to an "inverted" type at a critical thickness \(d_c\). We show that this transition is a topological quantum phase transition between a conventional insulating phase and a phase exhibiting the QSH effect with a single pair of helical edge states. We also discuss the methods for experimental detection of the QSH effect.
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              Chaotic Dirac billiard in graphene quantum dots

              We report on transport characteristics of quantum dot devices etched entirely in graphene. At large sizes, they behave as conventional single-electron transistors, exhibiting periodic Coulomb blockade peaks. For quantum dots smaller than 100 nm, the peaks become strongly non-periodic indicating a major contribution of quantum confinement. Random peak spacing and its statistics are well described by the theory of chaotic neutrino (Dirac) billiards. Short constrictions of only a few nm in width remain conductive and reveal a confinement gap of up to 0.5eV, which demonstrates the in-principle possibility of molecular-scale electronics based on graphene.
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                Author and article information

                Journal
                2016-04-13
                2016-04-18
                Article
                10.5772/64240
                1604.03783
                f5a331b2-80f1-4e9f-b5a4-a8a438c7ea1e

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                Typos corrected; hyperlinked references. 19 pages, 6 figures. A chapter submitted to "2D Materials", ISBN 978-953-51-4813-5, to be published by InTechOpen
                cond-mat.mes-hall

                Nanophysics
                Nanophysics

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