Diffusion of electrons in two-dimensional disordered symplectic systems

Kawarabayashi, Tohru; Ohtsuki, Tomi

doi:10.1103/physrevb.53.6975

Cited by 46 publications

(28 citation statements)

References 33 publications

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“…According to the single parameter scaling theory, this phase has a prefect conductivity. 3,20 This is in spite of the system being disordered. This conclusion might be avoided if there was some breakdown of single parameter scaling in the metallic regime.…”

Section: Summary and Discussionmentioning

confidence: 99%

Numerical estimation of theβfunction in two-dimensional systems with spin-orbit coupling

2004

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Section: Summary and Discussionmentioning

confidence: 99%

Numerical estimation of theβfunction in two-dimensional systems with spin-orbit coupling

2004

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“…This puts significant constraints on the system sizes that can be investigated numerically, and several approximations have been developed to circumvent these difficulties. One of them is to expand the evolution operator in terms of small-time increments 40 , or to study the time evolution of the position operator expanded in terms of Chebyshev polynomials combined with energy filtering via a Gaussian operator centered at a given energy and of the width of, e.g., 1% of the total bandwidth 41 . In the latter work, generalized quasiperiodic Rauzi tilings have been studied and the authors were interested how the topological connectivity of the tiling influences transport properties of the quasicrystal in d = 2, 3.…”

Section: Anomalous Diffusionmentioning

confidence: 99%

Spectral and diffusive properties of silver-mean quasicrystals in one, two, and three dimensions

2005

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Spectral properties and anomalous diffusion in the silver-mean (octonacci) quasicrystals in d = 1, 2, 3 are investigated using numerical simulations of the return probability C(t) and the width of the wave packet w(t) for various values of the hopping strength v. In all dimensions we find C(t) ∼ t −δ , with results suggesting a crossover from δ < 1 to δ = 1 when v is varied in d = 2, 3, which is compatible with the change of the spectral measure from singular continuous to absolute continuous; and we find w(t) ∼ t β with 0 < β(v) < 1 corresponding to anomalous diffusion. Results strongly suggest that β(v) is independent of d. The scaling of the inverse participation ratio suggests that states remain delocalized even for very small hopping amplitude v. A study of the dynamics of initially localized wavepackets in large three-dimensional quasiperiodic structures furthermore reveals that wavepackets composed of eigenstates from an interval around the band edge diffuse faster than those composed of eigenstates from an interval of the band-center states: while the former diffuse anomalously, the latter appear to diffuse slower than any power law.

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“…or the mean square displacement [18][19][20]27 d(t) = n |r n − r n 0 | 2 |Ψ n (t)| 2 1/2 (1.2) where Ψ n (t) is the amplitude of the wavefunction at time t at the nth site which is located at the position r n in space. Apparently, C(t) is the time-averaged probability of a wave packet staying at the initial site at time t, and d(t) determines the spreading of the width of a wave packet.…”

Section: Introductionmentioning

confidence: 99%

Energy spectra, wave functions, and quantum diffusion for quasiperiodic systems

et al. 2000

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We study energy spectra, eigenstates and quantum diffusion for one-and two-dimensional quasiperiodic tight-binding models. As our one-dimensional model system we choose the silver mean or "octonacci" chain. The twodimensional labyrinth tiling, which is related to the octagonal tiling, is derived from a product of two octonacci chains. This makes it possible to treat rather large systems numerically. For the octonacci chain, one finds singular continuous energy spectra and critical eigenstates which is the typical behaviour for one-dimensional Schrödinger operators based on substitution sequences. The energy spectra for the labyrinth tiling can, depending on the strength of the quasiperiodic modulation, be either band-like or fractallike. However, the eigenstates are multifractal. The temporal spreading of a wavepacket is described in terms of the autocorrelation function C(t) and the mean square displacement d(t). In all cases, we observe power laws C(t) ∼ t −δ and d(t) ∼ t β . For the octonacci chain, 0 < δ < 1, whereas for the labyrinth tiling a crossover is observed from δ = 1 to 0 < δ < 1 with increasing modulation strength. Corresponding to the multifractal eigenstates, we obtain anomalous diffusion with 0 < β < 1 for both systems. Moreover, we find that the behaviour of C(t) and d(t) is independent of the shape and the location of the initial wavepacket. We use our results to check several relations between the diffusion exponent β and the fractal dimensions of energy spectra and eigenstates that were proposed in the literature.

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Diffusion of electrons in two-dimensional disordered symplectic systems

Cited by 46 publications

References 33 publications

Numerical estimation of theβfunction in two-dimensional systems with spin-orbit coupling

Numerical estimation of theβfunction in two-dimensional systems with spin-orbit coupling

Spectral and diffusive properties of silver-mean quasicrystals in one, two, and three dimensions

Energy spectra, wave functions, and quantum diffusion for quasiperiodic systems

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