Experimental Observation of Quasicrystal Growth

Nagao, K.; Inuzuka, Tomoaki; Nishimoto, Kazue; Edagawa, Keiichi

doi:10.1103/physrevlett.115.075501

Cited by 57 publications

(48 citation statements)

References 15 publications

(31 reference statements)

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“…But as soon as this part is relaxed and stabilized, the defects will be corrected. This conjecture is consistent with the results of [1]. Our group has been working on a Hamiltonian model based on the empires of one dimensional and two dimensional quasicrystals.…”

Section: Discussionsupporting

confidence: 86%

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Methods for Calculating Empires in Quasicrystals

2017

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This paper reviews the empire problem for quasiperiodic tilings and the existing methods for generating the empires of the vertex configurations in quasicrystals, while introducing a new and more efficient method based on the cut-and-project technique. Using Penrose tiling as an example, this method finds the forced tiles with the restrictions in the high dimensional lattice (the mother lattice) that can be cut-and-projected into the lower dimensional quasicrystal. We compare our method to the two existing methods, namely one method that uses the algorithm of the Fibonacci chain to force the Ammann bars in order to find the forced tiles of an empire and the method that follows the work of N.G. de Bruijn on constructing a Penrose tiling as the dual to a pentagrid. This new method is not only conceptually simple and clear, but it also allows us to calculate the empires of the vertex configurations in a defected quasicrystal by reversing the configuration of the quasicrystal to its higher dimensional lattice, where we then apply the restrictions. These advantages may provide a key guiding principle for phason dynamics and an important tool for self error-correction in quasicrystal growth.

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Section: Discussionsupporting

confidence: 86%

“…When compared with regular crystals, quasicrystals present more complex structures and variations and have dynamic patterns that can be non-local due to the non-local nature of the quasicrystal itself [1]. Although not obvious, it is true that a given local patch of tiles in a quasicrystal can force tiles to lie in non-adjacent (non-local) positions.…”

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confidence: 99%

Methods for Calculating Empires in Quasicrystals

2017

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“…In addition, the prevalence of auxiliary information channels such as electron energy-loss spectra acquired at similar spatial resolutions allows one to append to these structural microstates additional chemical/electronic state information [2–4]. The data that emanate from such modalities reveal a wealth of information regarding the static modulation of material properties by local structural deviations [5], competing structural ground states [6], and even dynamic phase transformations or ensuing structural reordering during in situ atomic resolution imaging of materials growth [7]. These imaging modalities are crucial to fundamental investigations of modern materials, which often display a range of structural configurations and order parameter phases.…”

Section: Introductionmentioning

confidence: 99%

Identifying local structural states in atomic imaging by computer vision

Laanait

Ziatdinov

et al. 2016

Adv Struct Chem Imag

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The availability of atomically resolved imaging modalities enables an unprecedented view into the local structural states of materials, which manifest themselves by deviations from the fundamental assumptions of periodicity and symmetry. Consequently, approaches that aim to extract these local structural states from atomic imaging data with minimal assumptions regarding the average crystallographic configuration of a material are indispensable to advances in structural and chemical investigations of materials. Here, we present an approach to identify and classify local structural states that is rooted in computer vision. This approach introduces a definition of a structural state that is composed of both local and nonlocal information extracted from atomically resolved images, and is wholly untethered from the familiar concepts of symmetry and periodicity. Instead, this approach relies on computer vision techniques such as feature detection, and concepts such as scale invariance. We present the fundamental aspects of local structural state extraction and classification by application to simulated scanning transmission electron microscopy images, and analyze the robustness of this approach in the presence of common instrumental factors such as noise, limited spatial resolution, and weak contrast. Finally, we apply this computer vision-based approach for the unsupervised detection and classification of local structural states in an experimental electron micrograph of a complex oxides interface, and a scanning tunneling micrograph of a defect-engineered multilayer graphene surface.Electronic supplementary materialThe online version of this article (doi:10.1186/s40679-016-0028-8) contains supplementary material, which is available to authorized users.

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“…The Bragg diffraction peaks of quasicrystals possess rotational symmetries such as 5, 7, 8, 9, 10-fold that are forbidden in classical crystalline orders [1,2]. Since its first report in Al-Mn and Al-Mn-Si alloys in 1984 [3], quasicrystal order has been studied and discovered in many different materials [4][5][6][7][8][9][10].Supersolid, another exotic phase of matter, combines solid crystalline structure with superfluidity, where two continuous symmetries, namely, translational and U (1) gauge, are spontaneously broken [11]. Supersolids were first predicted for helium almost 50 years ago [12,13], and have recently been observed in cold atom experiments [14,15], where a stripe phase with supersolid properties was generated and observed in a Bose-Einstein condensate (BEC) [14].…”

mentioning

confidence: 99%

mentioning

confidence: 99%

Superfluid-Quasicrystal in a Bose-Einstein Condensate

Hou

Sun

et al. 2018

Phys. Rev. Lett.

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Quasicrystal is a class of ordered structures defying conventional classification of solid crystals and may carry classically forbidden (e.g., 5-fold) rotational symmetries. In view of long-sought supersolids, a natural question is whether a superfluid can spontaneously form quasicrystalline order that is not possessed by the underlying Hamiltonian, forming "super-quasicrystals". Here we show that a super-quasicrystal stripe state with the minimal 5-fold rotational symmetry can be realized as the ground state of a Bose-Einstein condensate within a practical experimental scheme. There exists a rich phase diagram consisting of various super-quasicrystal, supersolid, and plane-wave phases. Our scheme can be generalized for generating other higher-order (e.g., 7-fold) quasicrystal states, and provides a platform for investigating such new exotic quantum matter.Introduction. Quasicrystals exhibit exotic spatial patterns that are neither periodic as solid crystals (i.e., lack of translational symmetry) nor totally disordered (i.e., possession of long-range order) [1]. The Bragg diffraction peaks of quasicrystals possess rotational symmetries such as 5, 7, 8, 9, 10-fold that are forbidden in classical crystalline orders [1,2]. Since its first report in Al-Mn and Al-Mn-Si alloys in 1984 [3], quasicrystal order has been studied and discovered in many different materials [4][5][6][7][8][9][10].Supersolid, another exotic phase of matter, combines solid crystalline structure with superfluidity, where two continuous symmetries, namely, translational and U (1) gauge, are spontaneously broken [11]. Supersolids were first predicted for helium almost 50 years ago [12,13], and have recently been observed in cold atom experiments [14,15], where a stripe phase with supersolid properties was generated and observed in a Bose-Einstein condensate (BEC) [14]. These great advances in the study of supersolids raise a natural question: is it possible to create a novel quantum matter where both superfluidity and quasicrystal orders coexist?In this Letter, we address this important question by proposing a scheme to generate a stable quasicrystal ground state in a BEC. The experimental setup contains a 3D BEC confined in a 1D optical superlattice with quintuple well (defines 5 pseudospin states), where neighboring wells are coupled by Raman assisted tunneling to generate an effective spin-orbit coupling (SOC) in the perpendicular plane. The scheme utilizes natural contact interaction and can realize quasicrystals with the minimum 5-fold rotational symmetry. In this new quantum state, the U (1) gauge symmetry is spontaneously broken just as that in supersolid stripe phases [14,16]. However, the discrete translational symmetry, which is preserved in supersolids, has also been broken, leaving only specified rotational symmetry. A quasicrystal order with such rotational symmetry is spontaneously formed although the underlying Hamiltonian does not possess such order. Therefore we denote this quantum matter as 'super-quasicrystal'. By tuning syste...

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Experimental Observation of Quasicrystal Growth

Cited by 57 publications

References 15 publications

Methods for Calculating Empires in Quasicrystals

Methods for Calculating Empires in Quasicrystals

Identifying local structural states in atomic imaging by computer vision

Superfluid-Quasicrystal in a Bose-Einstein Condensate

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