Spectral properties of superconducting microwave photonic crystals modeling Dirac billiards

Dietz, Barbara; Klaus, T.; Miski-Oglu, Maksym; Richter, A.

doi:10.1103/physrevb.91.035411

Cited by 44 publications

(84 citation statements)

References 58 publications

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“…Quite recently, the Dirac stadium was experimentally studied with the aid of microwave resonators in Refs. [35,36]. Motivated by [34] and other findings, 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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“…Quite recently, the Dirac stadium was experimentally studied with the aid of microwave resonators in Refs. [35,36]. Motivated by [34] and other findings, Ref.…”

Section: Introductionmentioning

confidence: 99%

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

2016

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“…Accordingly, it is sufficient to consider only states corresponding to positive energy values, 0 < ∼ E/t ≤ 3. The quasiparticles in graphene exhibit distinct behaviors in different energy ranges [13]. In particular, in the lower energy range close to the Dirac point, E/t ∈ [0.02, 0.2], the quasiparticles are described by the two-dimensional Dirac equation for massless Dirac fermions with little trigonal warping so that the corresponding motion is isotropic.…”

Section: Modelmentioning

confidence: 99%

“…4 (c). Actually, in these energy ranges the quasimomenta of the graphene billiard may be identified with the low-energy eigenwavevectors of the corresponding quantum billiards [13]. Accordingly, close to the band edges, the effective wavelengths are long compared to the distances between the neighboring atoms and the lengths of the armchair and zigzag line-segments along the boundaries.…”

Section: Fig 4 Intensity Distributions In the 15mentioning

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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“…At the same time, the development of superconducting microwave billiards [6,7] and of photonic crystals [8,9] combined into "microwave photonic crystals", or generally, of "artificial graphene" [10][11][12][13][14][15][16][17][18][19][20], has opened the way for simulations of crystal vibrations in systems of lower dimensionality (2D, 1D, 0D) with a finite number of units.…”

Section: Introductionmentioning

confidence: 99%

Algebraic theory of crystal vibrations: Singularities and zeros in vibrations of one- and two-dimensional lattices

et al. 2015

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A novel method for the calculation of the energy dispersion relation (EDR) and density of states (DOS) in one (1D) and two (2D) dimensions is introduced and applied to linear lattices (1D) and square and hexagonal lattices (2D). The (van Hove) singularities and (Dirac) zeros of the DOS are discussed. Results for the 2D hexagonal lattice (graphene-like materials) are compared with experimental data in microwave photonic crystals.

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Spectral properties of superconducting microwave photonic crystals modeling Dirac billiards

Cited by 44 publications

References 58 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

Algebraic theory of crystal vibrations: Singularities and zeros in vibrations of one- and two-dimensional lattices

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