Topological Materials Discovery from Crystal Symmetry

Wieder, Benjamin J.; Bradlyn, Barry; Cano, Jennifer; Wang, Zhijun; Vergniory, Maia G.; Elcoro, Luis; Soluyanov, Alexey A.; Felser, Claudia; Neupert, Titus; Regnault, Nicolas; Bernevig, B. Andrei

doi:10.48550/arxiv.2106.00709

Cited by 6 publications

(10 citation statements)

References 332 publications

(830 reference statements)

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“…These modes correspond to quantized higher electric multipole moments, and because of this unusual bulk-boundary correspondence they are often re-ferred to as higher-order TIs (HOTIs) [26][27][28][29][30][31][32][33][34], in contrast to the previously mentioned first-order TIs. Their theoretical prediction has been quickly matched with the first experimental realizations, with HOTIs realized in bismuth [35,36], topolectrical circuits [37][38][39][40][41][42], photonic crystals [43][44][45], acoustic [46][47][48] and elastic systems [42]. Usually one considers first-and higher-order topology as exclusive: either one or the other is realized.…”

Section: Introductionmentioning

confidence: 76%

Competition of First-Order and Second-Order Topology on the Honeycomb Lattice

Bunney,

Mizoguchi,

Hatsugai

et al. 2021

Preprint

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We investigate both first-order topology, as realized through Haldane's model, and second-order topology, implemented through an additional Kekulé-distortion, on the honeycomb lattice. The interplay and competition of both terms result in a phase diagram at half-filling which contains twelve distinct phases. All phases can be characterized by the first Chern number or by a quantized Z Q Berry phase. Highlights include phases with high Chern numbers, a novel Z6 topological phase, but also coupled kagome-lattice Chern insulators. Furthermore, we explore the insulating phases at lower fillings, and find again first-order and second-order topological phases. Finally, we identify real-space structures which feature corner states not only at half but also at third and sixth fillings, in agreement with the quantized Z Q Berry phases.

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Section: Introductionmentioning

confidence: 76%

Competition of First-Order and Second-Order Topology on the Honeycomb Lattice

Bunney,

Mizoguchi,

Hatsugai

et al. 2021

Preprint

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“…where N is the number of filled bands and [M 1 2 ] is the difference in the number of times the co-irrep E 1 2 appears at M = (π, π) and at Γ = (0, 0) in the valence bands. (The little co-group of both Γ and M is 4/m ; its co-irreps are listed in Table I.)…”

Section: Symmetry Indicators For Filling Anomaliesmentioning

confidence: 99%

“…). Since a crossing between the two co-irreps changes [M 1 2 ] by ±1, it results in a change ∆η (4) = ±2. Since η (4) is a mod 4 quantity, ∆η (4) is also defined mod 4.…”

Section: Classification Of Dirac Pointsmentioning

confidence: 99%

“…(Notice this BZ is the same as that of P 6/m, but the little co-groups are different; for example, the high symmetry line (−4π/3, 0, −k z ) is mapped to (4π/3, 0, k z ) under inversion symmetry.) The little co-group of both ∆ and P is 3 , which has two two-dimensional co-irreps, E 1 2 and E 3 2 . A crossing between the two co-irreps along either the high symmetry line ∆ and P changes the filling anomaly by ∆η (3) = ±2 mod 6.…”

Section: N =mentioning

confidence: 99%

“…Topological semimetals encompass a large family of materials exhibiting band crossings near the Fermi level [1], such as Weyl [2][3][4][5][6][7][8][9], Dirac [10][11][12][13][14] and multifold fermions [15][16][17]. One of the novel features of Weyl and other chiral semimetals is their bulk-edge correspondence in the form of surface Fermi arcs [2].…”

Section: Introductionmentioning

confidence: 99%

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Classification of Dirac points with higher-order Fermi arcs

Fang,

Cano

2021

Preprint

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Dirac semimetals lack a simple bulk-boundary correspondence. Recently, Dirac materials with four-fold rotation symmetry have been shown to exhibit a higher order bulk-hinge correspondence: they display "higher order Fermi arcs," which are localized on hinges where two surfaces meet and connect the projections of the bulk Dirac points. In this paper, we classify higher order Fermi arcs for Dirac semimetals protected by a rotation symmetry and the product of time-reversal and inversion. Such Dirac points can be either linear in all directions or linear along the rotation axis and quadratic in other directions. By computing the filling anomaly for momentum-space planes on either side of the Dirac point, we find that all linear Dirac points exhibit higher order Fermi arcs terminating at the projection of the Dirac point, while the Dirac points that are quadratic in two directions lack such higher order Fermi arcs. When higher order Fermi arcs do exist, they obey either a Z2 (four-fold rotation axis) or Z3 (three-or six-fold rotation axis) group structure. Finally, we build two models with six-fold symmetry to illustrate the cases with and without higher order Fermi arcs. We predict higher order Fermi arcs in Na3Bi.

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Machine Learning-Augmented Spectroscopies for Intelligent Materials Design

Andrejevic

2022

Springer Theses

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Neutron and photon scattering and spectroscopy represent two fundamental categories of characterization techniques used to interrogate materials' structural and dynamical properties at atomic to mesoscopic length scales. As advances at scientific user facilities enable the collection of ever larger data volumes in higher-dimensional parameter spaces, the design, analysis, and interpretation of such experiments becomes both increasingly valuable and complex. At the same time, interest in novel functional and quantum materials for next-generation technologies, including dissipationless electronics, energy harvesting, and quantum computing, demands an understanding of unconventional or emergent properties beyond the scope of many approximate models. Machine learning methods are designed to leverage large, highdimensional datasets in order to detect underlying patterns and make informed predictions on related tasks. Thus, integration of these data-driven methods with neutron and photon spectroscopies has the potential to improve experimental design, accelerate and enhance data analysis, and uncover insights beyond traditional models.This thesis work demonstrates the proposed integration of machine learning to augment experimental design and analysis in the context of four different scattering and spectroscopic techniques. First, we use Euclidean neural networks to predict materials' vibrational properties directly from the atomic masses and positions of their constituent atoms, highlighting the importance of using effective materials data representations to strengthen model performance and interpretability. We then consider how machine learning methods can be applied to develop effective, low-dimensional representations of materials' spectral signatures, which we exemplify through unsupervised representation learning of Raman spectra. Such learned representations are proposed as efficient prediction targets for supervised learning from relevant structural or chemical attributes, or as convenient parameter spaces for optimization of physical models. We illustrate the latter by training a variational autoencoder to retrieve the sample parameters of proximity-coupled heterostructures from their polarized neutron reflectometry profiles with high resolution. Finally, we study the capacity of machine learning models to extract "hidden" insights from spectral data by develop-

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Topological Materials Discovery from Crystal Symmetry

Cited by 6 publications

References 332 publications

Competition of First-Order and Second-Order Topology on the Honeycomb Lattice

Competition of First-Order and Second-Order Topology on the Honeycomb Lattice

Classification of Dirac points with higher-order Fermi arcs

Machine Learning-Augmented Spectroscopies for Intelligent Materials Design

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