Symmetry-based indicators of band topology in the 230 space groups

Po, Hoi Chun; Vishwanath, Ashvin; Watanabe, Haruki

doi:10.1038/s41467-017-00133-2

Cited by 760 publications

(926 citation statements)

References 48 publications

(161 reference statements)

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“…This local approach obfuscates any connection to band topology, which requires understanding how these different localized descriptions fit together to make a global band structure. While there has been some recent work towards addressing how symmetry constrains global band structures [14,15], a complete and constructive approach to the problem has not yet been presented.…”

mentioning

confidence: 99%

Graph theory data for topological quantum chemistry

et al. 2017

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mentioning

confidence: 99%

Graph theory data for topological quantum chemistry

et al. 2017

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“…The authors designed what is known as the first catalog of topological electronic materials. In the same spirit, using the recently developed symmetry indicators method [363], Tanget al found 258 TIs and 165 topological crystalline insulators which have robust topological character [359], i.e., considerable full or direct band gap. The authors also found 489 topological semimetals with the band crossing points located near the Fermi level [359].…”

Section: Topological Ordered Materialsmentioning

confidence: 97%

From DFT to machine learning: recent approaches to materials science–a review

et al. 2019

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Recent advances in experimental and computational methods are increasing the quantity and complexity of generated data. This massive amount of raw data needs to be stored and interpreted in order to advance the materials science field. Identifying correlations and patterns from large amounts of complex data is being performed by machine learning algorithms for decades. Recently, the materials science community started to invest in these methodologies to extract knowledge and insights from the accumulated data. This review follows a logical sequence starting from density functional theory as the representative instance of electronic structure methods, to the subsequent high-throughput approach, used to generate large amounts of data. Ultimately, data-driven strategies which include data mining, screening, and machine learning techniques, employ the data generated. We show how these approaches to modern computational materials science are being used to uncover complexities and design novel materials with enhanced properties. Finally, we point to the present research problems, challenges, and potential future perspectives of this new exciting field. characterized by its diverse and huge volume, usually ranging from terabytes to petabytes of data, being created in or near real-time. Such data is found either structured and unstructured in nature, and is exhaustive, usually aiming to capture entire populations in a scalable manner [7]. Simple tasks represent challenges in this scale: capture, curation, storage, search, sharing, analysis, and visualization of the data cannot be accomplished without the proper tools. Thus, it can be effectively summarized by the popular 'five V's': volume, velocity, variety, veracity, and value, shown in figure 3(right). A related sixth V is visualization, although not exclusive to Big Data, which requires different techniques to handle data with various characteristics.Striving to tackle the challenges imposed by Big Data, the field of Data Science has arisen. It is largely interdisciplinary being a combination of mathematics and statistics, computer science and programming, and domain knowledge for problem definition and solving, as shown in figure 3(left). Its objective is, roughly speaking, to deal with the whole process of data production, cleaning, preparation, and finally, analysis. Data science encompasses areas such as Big Data, which deals with large volumes of data, and data mining, which relates to analysis processes to discover patterns and extract knowledge from data, part of the so-called Knowledge Discovery in Databases (KDD).The analysis process within Data Science is challenging, as the techniques are very different from traditional static and rigid datasets, generated and analyzed under a predetermined hypothesis. The distinction from traditional data is based on the larger abundance, exhaustivity, and variety of Big Data. It is also much more dynamic, messy and uncertain, being highly relational [7]. Recently, the possibility of overcoming such a challenge slowly sta...

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“…As a result, the system evolves into an AFM topological (crystalline) insulator with a massive bulk Dirac cone as shown in Figure a,b. Due to the presence of a band gap in the bulk and the preserved

scriptP

symmetry, it is possible to calculate the topological parity‐based invariant Z 4 index, which is defined as

Z_{4} = \sum_{i = 1}^{8} \sum_{n = 1}^{n_{occ}} \frac{1 + ξ_{n} (K_{i})}{2}

mod 4 33. From the calculated band structure of EuCd 2 As 2 , we obtained Z 4 = 2.…”

Section: The Number Of Occupied Bands With Even and Odd Parity At Thementioning

confidence: 99%

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂

Wang

Nie

et al. 2020

Advanced Materials

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Parity‐time symmetry plays an essential role for the formation of Dirac states in Dirac semimetals. So far, all of the experimentally identified topologically nontrivial Dirac semimetals (DSMs) possess both parity and time reversal symmetry. The realization of magnetic topological DSMs remains a major issue in topological material research. Here, combining angle‐resolved photoemission spectroscopy with density functional theory calculations, it is ascertained that band inversion induces a topologically nontrivial ground state in EuCd2As2. As a result, ideal magnetic Dirac fermions with simplest double cone structure near the Fermi level emerge in the antiferromagnetic (AFM) phase. The magnetic order breaks time reversal symmetry, but preserves inversion symmetry. The double degeneracy of the Dirac bands is protected by a combination of inversion, time‐reversal, and an additional translation operation. Moreover, the calculations show that a deviation of the magnetic moments from the c‐axis leads to the breaking of C3 rotation symmetry, and thus, a small bandgap opens at the Dirac point in the bulk. In this case, the system hosts a novel state containing three different types of topological insulator: axion insulator, AFM topological crystalline insulator (TCI), and higher order topological insulator. The results provide an enlarged platform for the quest of topological Dirac fermions in a magnetic system.

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Symmetry-based indicators of band topology in the 230 space groups

Cited by 760 publications

References 48 publications

Graph theory data for topological quantum chemistry

Graph theory data for topological quantum chemistry

From DFT to machine learning: recent approaches to materials science–a review

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂

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Symmetry-based indicators of band topology in the 230 space groups

Cited by 760 publications

References 48 publications

Graph theory data for topological quantum chemistry

Graph theory data for topological quantum chemistry

From DFT to machine learning: recent approaches to materials science–a review

Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd2As2

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Emergence of Nontrivial Low‐Energy Dirac Fermions in Antiferromagnetic EuCd₂As₂