Hofstadter butterfly of a quasicrystal

Fuchs, Jean-Noël; Vidal, Julien

doi:10.1103/physrevb.94.205437

Cited by 54 publications

(51 citation statements)

References 44 publications

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“…Direct approaches such as diagonalization of the full Hamiltonian are computationally intractable because of the large basis required to fully capture the structure. Although some one-dimensional nonperiodic systems have been solved [39][40][41], few two-dimensional systems have been solved [42][43][44][45]. As such, solving for the singleparticle and many-particle eigenstates of the quasicrystal potential is beyond the scope of this article.…”

Section: Background and Motivationmentioning

confidence: 99%

Two-dimensional optical quasicrystal potentials for ultracold atom experiments

Corcovilos

Mittal

2019

Appl. Opt.

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Quasicrystals are nonperiodic structures having no translational symmetry but nonetheless possessing long-range order. The material properties of quasicrystals, particularly their low-temperature behavior, defy easy description. We present a compact optical setup for creating quasicrystal optical potentials with 5-fold symmetry using interference of nearly co-propagating beams for use in ultracold atom quantum simulation experiments. We verify the optical design through numerical simulations and demonstrate a prototype system. We also discuss generating phason excitations and quantized transport in the quasicrystal through phase modulation of the beams.

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Section: Background and Motivationmentioning

confidence: 99%

Two-dimensional optical quasicrystal potentials for ultracold atom experiments

Corcovilos

Mittal

2019

Appl. Opt.

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“…More specifically, we consider tilings made of plaquettes with rational areas, such as the commensurate version of the Rauzy tiling [11], of the octagonal (or Ammann-Beenker) tiling [12] and of the Penrose tiling [13]. We also consider a random tiling obtained from the commensurate Rauzy tiling by phason flips (geometric disorder) [7]. We then numerically diagonalize the Hamiltonian of these tight-binding models for each flux compatible with periodic boundary conditions (PBC) in order to obtain the energy spectrum as a function of the applied perpendicular magnetic field, known as a Hofstadter butterfly (see Ref.…”

Section: Hofstadter Butterfly Of Quasicrystalsmentioning

confidence: 99%

“…We then numerically diagonalize the Hamiltonian of these tight-binding models for each flux compatible with periodic boundary conditions (PBC) in order to obtain the energy spectrum as a function of the applied perpendicular magnetic field, known as a Hofstadter butterfly (see Ref. [7] for details).…”

Section: Hofstadter Butterfly Of Quasicrystalsmentioning

confidence: 99%

“…For a convenient gauge choice adapted to this problem, we refer the interested reader to Ref. [7]. The energy spectrum is then obtained by numerical diagonalization of the Hamiltonian as a function of the allowed fluxes f .…”

Section: Hofstadter Butterfly Of Quasicrystalsmentioning

confidence: 99%

“…We have recently computed the Hofstadter butterfly for a quasiperiodic tiling (Rauzy tiling) and also for a random tiling [7]. In both cases, LLs have been found near band edges and at low magnetic field.…”

Section: Introductionmentioning

confidence: 99%

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Landau levels in quasicrystals

2018

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Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge near band edges in the zero-field limit. Their existence is related to an effective zero-field dispersion relation valid in the continuum limit. For quasicrystals studied here, an underlying periodic crystal exists and provides a natural interpretation to this dispersion relation. In addition to the slope (effective mass) of Landau levels, we also study their width as a function of the magnetic flux and identify two fundamental broadening mechanisms: (i) tunneling between closed cyclotron orbits and (ii) individual energy displacement of states within a Landau level. Interestingly, the typical broadening of the Landau levels is found to behave algebraically with the magnetic field with a nonuniversal exponent. PACS numbers: 71.23.Ft,71.70.Di,73.43.-f 1 These commensurate quasicrystals have perfect long-range order and are no less quasicrystalline than the original ones. The adjective "commensurate" only refers to the fact that the ratios of their plaquette areas are rational numbers. arXiv:1807.10032v2 [cond-mat.dis-nn]

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Interface Characterization and Control of 2D Materials and Heterostructures

2018

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2D materials and heterostructures have attracted significant attention for a variety of nanoelectronic and optoelectronic applications. At the atomically thin limit, the material characteristics and functionalities are dominated by surface chemistry and interface coupling. Therefore, methods for comprehensively characterizing and precisely controlling surfaces and interfaces are required to realize the full technological potential of 2D materials. Here, the surface and interface properties that govern the performance of 2D materials are introduced. Then the experimental approaches that resolve surface and interface phenomena down to the atomic scale, as well as strategies that allow tuning and optimization of interfacial interactions in van der Waals heterostructures, are systematically reviewed. Finally, a future outlook that delineates the remaining challenges and opportunities for 2D material interface characterization and control is presented.

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Hofstadter butterfly of a quasicrystal

Cited by 54 publications

References 44 publications

Two-dimensional optical quasicrystal potentials for ultracold atom experiments

Two-dimensional optical quasicrystal potentials for ultracold atom experiments

Landau levels in quasicrystals

Interface Characterization and Control of 2D Materials and Heterostructures

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