Quantum chaotic scattering in graphene systems

Yang, Rui; Huang, Liang; Lai, Ying–Cheng; Grebogi, Celso

doi:10.1209/0295-5075/94/40004

Cited by 39 publications

(70 citation statements)

References 41 publications

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“…Among the different electronic Dirac devices, the chaotic Dirac quantum dot (DQD), also called chaotic Dirac billiard (DB), has received a significant highlight [4,18,[24][25][26][27][28][29][30][31][32][33], due to its universal characteristics. In the search for such universal properties, the Ref.…”

Section: Introductionmentioning

confidence: 99%

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

2016

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We develop the stub model for the Dirac Quantum Dot, an electron confining device on a grapheme surface. Analytical results for the average conductance and the correlation functions are obtained and found in agreement with those found previously using semiclassical calculation. Comparison with available data are presented. The results reported here demonstrate the applicability of Random Matrix Theory in the case of Dirac electrons confined in a stadium.

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Section: Introductionmentioning

confidence: 99%

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

2016

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“…Generally, the interplay between different types of classical dynamics and relativistic quantum mechanics can lead to surprising phenomena. For example, in open Hamiltonian systems such as graphene quantum dots, previous works revealed that chaos has relatively weaker effects on the quantum scattering dynamics as compared with the nonrelativistic quantum counterpart [77,78]. For example, when the classical dynamics of a quantum dot is integrable or mixed, there are sharp transmission resonances.…”

Section: Discussionmentioning

confidence: 99%

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards

et al. 2016

Phys. Rev. E

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A crucial result in quantum chaos, which has been established for a long time, is that the spectral properties of classically integrable systems generically are described by Poisson statistics whereas those of time-reversal symmetric, classically chaotic systems coincide with those of random matrices from the Gaussian orthogonal ensemble (GOE). Does this result hold for two-dimensional Dirac material systems? To address this fundamental question, we investigate the spectral properties in a representative class of graphene billiards with shapes of classically integrable circular-sector billiards. Naively one may expect to observe Poisson statistics, which is indeed true for energies close to the band edges where the quasiparticle obeys the Schrödinger equation. However, for energies near the Dirac point, where the quasiparticles behave like massless Dirac fermions, Poisson statistics is extremely rare in the sense that it emerges only under quite strict symmetry constraints on the straight boundary parts of the sector. An arbitrarily small amount of imperfection of the boundary results in GOE statistics. This implies that, for circular sector confinements with arbitrary angle, the spectral properties will generically be GOE. These results are corroborated by extensive numerical computation. Furthermore, we provide a physical understanding for our results.

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“…In the past decade, due to the tremendous development of the science of 2D Dirac materials initiated by the experimental realization of graphene [8][9][10][11][12]57,58 , relativistic quantum manifestations of classical chaos 59 have emerged as a new field of study 39,[60][61][62][63][64][65] , with the basic goal to uncover and understand the possible role of chaos played in relativistic quantum systems. From a practical point of view, exploiting the interplay between chaos and relativistic quantum mechanics can lead to novel ideas for developing electronic devices.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…The shape of the scattering region is that of the cosine billiard [36][37][38][39] with an upper and a lower hard boundaries at y(x) = W + (M/2)[1 − cos (2πx/L − π)] and y = 0, respectively, for −L/2 ≤ x ≤ L/2. To make the scattering region symmetrical, we choose the lower boundary to be y(…”

Section: Introductionmentioning

confidence: 99%

Enhancement of spin polarization by chaos in graphene quantum dot systems

Ying

Lai

2016

Phys. Rev. B

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When graphene is placed on a substrate of heavy metal, Rashba spin-orbit interaction of substantial strength can occur. In an open system such as a quantum dot, the interaction can induce spin polarization. Would classical dynamics have any effect on the spin polarization? Here we consider the quantum-dot setting, where the Rashba interaction is confined within the central scattering region whose geometrical shape can be chosen to yield distinct types of dynamics, e.g., regular or chaotic, in the classical limit. We find that, as compared with regular or mixed dynamics, chaos can lead to significantly smooth fluctuation patterns of the spin polarization in its variation with the Fermi energy. Strikingly, in the experimentally feasible range of the Rashba interaction strength, the average polarization for a chaotic dot can be markedly larger than that for a regular or mixed dot. From the semiclassical viewpoint, a key quantity that determines the average spin polarization is the angle distribution of the outgoing electrons at the interface between regions with and without the Rashba interaction, respectively. Classical chaos generates a different distribution which, in turn, leads to higher average spin polarization. There was little previous work on the interplay between classical chaos and electron spin, and the phenomenon of chaos-enhanced spin polarization uncovered here can be exploited for spintronics applications.

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Quantum chaotic scattering in graphene systems

Cited by 39 publications

References 41 publications

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

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

Gaussian orthogonal ensemble statistics in graphene billiards with the shape of classically integrable billiards

Enhancement of spin polarization by chaos in graphene quantum dot systems

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