Hyperuniform electron distributions controlled by electron interactions in quasicrystals

Sakai, Shiro; Arita, Ryotaro; Ohtsuki, Tomi

doi:10.1103/physrevb.105.054202

Cited by 13 publications

(8 citation statements)

References 60 publications

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“…We first show that they are indeed hyperuniform and belong to Class I. We then compute the order metric and show that it changes significantly with the introduction of the electron interactions, similarly to our previous results on the Penrose tiling [10].…”

Section: Introductionsupporting

confidence: 65%

“…This gives a strong modulation of the electron distribution {n i }. The Hartree term of U and the Fock term of V also give site-dependent effects, but their effects are relatively small [10,18].…”

Section: Calculation Of the Charge Distributionmentioning

confidence: 99%

“…We then analyze the charge distribution in terms of the hyperuniformity [11,12], as we did for the Penrose tiling in Ref. [10]. We first plot in Fig.…”

Section: Hyperuniformitymentioning

confidence: 99%

“…In Ref. [10], the author showed that the charge distribution on the Penrose tiling is hyperuniform, and its change can be characterized by the change of the order metric of the hyperuniformity. Hyperuniformity, coined by Torquato and his collaborators [11,12], is a framework to quantify the distribution of various point sets in a space and has been generalized to a scalar field [13,14].…”

Section: Introductionmentioning

confidence: 99%

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Hyperuniform electron distributions on the Ammann-Beenker tiling

Sakai

2023

J. Phys.: Conf. Ser.

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We study the electron charge distribution on a quasiperiodic tiling in terms of hyperuniformity. In an extended Hubbard model on the Ammann-Beenker tiling, the electron distribution changes significantly with the Fermi energy and electron-interaction strength. Unlike periodic systems, these changes are not characterized by translational-symmetry breaking. We show that the electron charge distribution is not characterized by multifractality, either. We find that the distribution is instead characterized by hyperuniformity of Class I.

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Section: Introductionsupporting

confidence: 65%

Section: Calculation Of the Charge Distributionmentioning

confidence: 99%

“…We then analyze the charge distribution in terms of the hyperuniformity [11,12], as we did for the Penrose tiling in Ref. [10]. We first plot in Fig.…”

Section: Hyperuniformitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Hyperuniform electron distributions on the Ammann-Beenker tiling

Sakai

2023

J. Phys.: Conf. Ser.

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“…Finally, the eigenstate correlation functions, and their evolution under disorder, have implications for numerous other electronic properties of tilings. The effects of disorder on the charge distributions studied in [58], on Kondo screening of impurities [59], valence fluctuations [60], or properties of superconducting [61,62] and magnetic phases [63,64] have not been addressed, with the exception of phason disorder effects in a Heisenberg antiferromagnet [65]. It would be interesting to study how the charge distribution evolves with disorder.…”

Section: Discussionmentioning

confidence: 99%

Electronic states of a disordered 2D quasiperiodic tiling: from critical states to Anderson localization

Jagannathan¹,

Tarzia²

2022

Preprint

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We consider critical eigenstates in a two dimensional quasicrystal and their evolution as a function of disorder. By exact diagonalization of finite size systems we show that the evolution of the spectral properties of a typical wavefunction is non-monotonic. That is, disorder leads to states delocalizing, until a certain crossover disorder strength is attained, after which they start to localize. This non-monotonic evolution of spatial properties of eigenstates can be observed in the anomalous dimensions of the wavefunction amplitudes, in their multifractal spectra, and in their dynamical properties. We compute the two-point correlation functions of wavefunction amplitudes and show that these follow power laws in distance and energy, consistent with the idea that wavefunctions retain their multifractal structure on a scale which depends on disorder strength. Finally dynamical properties are studied as a function of disorder. We find that the diffusion exponents do not reflect the non-monotonic wavefunction evolution. Instead, they are essentially independent of disorder until disorder increases beyond the crossover value, after which they decrease rapidly, until the strong localization regime is reached. The differences between our results and earlier studies on geometrically disordered "phason-flip" models lead us to propose that the two models are in different universality classes. We conclude by discussing some implications of our results for transport and a proposal for a Mott hopping mechanism between power law localized wavefunctions, in moderately disordered quasicrystals.

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Properties of the Ammann–Beenker Tiling and its Square Periodic Approximants

Jagannathan,

Duneau

2024

Israel Journal of Chemistry

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Our understanding of physical properties of quasicrystals owes a great deal to studies of tight‐binding models constructed on quasiperiodic tilings. Among the large number of possible quasiperiodic structures, two dimensional tilings are of particular importance – in their own right, but also for information regarding properties of three dimensional systems. We provide here a users manual for those wishing to construct and study physical properties of the 8‐fold Ammann–Beenker quasicrystal, a good starting point for investigations of two dimensional quasiperiodic systems. This tiling has a relatively straightforward construction. Thus, geometrical properties such as the type and number of local environments can be readily found by simple analytical computations. Transformations of sites under discrete scale changes – called inflations and deflations – are easier to establish compared to the celebrated Penrose tiling, for example. We have aimed to describe the methodology with a minimum of technicalities but in sufficient detail so as to enable non‐specialists to generate quasiperiodic tilings and periodic approximants, with or without disorder. The discussion of properties includes some relations not previously published, and examples with figures.

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Hyperuniform electron distributions controlled by electron interactions in quasicrystals

Cited by 13 publications

References 60 publications

Hyperuniform electron distributions on the Ammann-Beenker tiling

Hyperuniform electron distributions on the Ammann-Beenker tiling

Electronic states of a disordered 2D quasiperiodic tiling: from critical states to Anderson localization

Properties of the Ammann–Beenker Tiling and its Square Periodic Approximants

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