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Although the richness of spatial symmetries has led to a rapidly expanding inventory of possible topological crystalline (TC) phases of electrons, physical realizations have been slow to materialize due to the practical difficulty to…

Mesoscale and Nanoscale Physics · Physics 2019-05-14 Feng Tang , Hoi Chun Po , Ashvin Vishwanath , Xiangang Wan

"Topological Quantum Chemistry (TQC) links the chemical and symmetry structure of a given material with its topological properties. This field tabulates the data of the 10398 real-space atomic limits of materials, and solves the…

Materials Science · Physics 2019-11-15 M. G. Vergniory , L. Elcoro , C. Felser , N. Regnault , B. A. Bernevig , Z. Wang

Crystalline symmetries play an important role in the classification of band structures, and the rich variety of spatial symmetries in solids leads to various topological crystalline phases (TCPs). However, compared with topological…

Mesoscale and Nanoscale Physics · Physics 2019-03-12 Feng Tang , Hoi Chun Po , Ashvin Vishwanath , Xiangang Wan

Topological materials in crystal solids, including topological insulators (TIs), topological crystalline insulators (TCIs), topological Dirac semimetals (DSMs), topological Weyl semimetals (WSMs), topological Dirac or Weyl nodal line…

Materials Science · Physics 2017-05-05 Xing-Qiu Chen

Topological Quantum Chemistry and Symmetry-Based Indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy ($E_{F}$). We report the completion of a publicly accessible catalog of stable…

Topological materials (TMs) showcase intriguing physical properties defying expectations based on conventional materials, and hold promise for the development of devices with new functionalities. While several theoretically proposed TMs…

Mesoscale and Nanoscale Physics · Physics 2019-04-19 Feng Tang , Hoi Chun Po , Ashvin Vishwanath , Xiangang Wan

The recent discovery of topological insulators has revived interest in the topological properties of insulating band structures. In this work, we extend the topological classification of insulating band structures to include certain point…

Materials Science · Physics 2011-03-15 Liang Fu

One of the most significant breakthroughs in physics of the last decade has been the discovery that materials with non-trivial topological properties for electronic, electromagnetic, acoustic and mechanical responses can be designed and…

Optics · Physics 2022-11-21 Xiang Ni , Simon Yves , Alex Krasnok , Andrea Alu

The first-principles band theory paradigm has been a key player not only in the process of discovering new classes of topologically interesting materials, but also for identifying salient characteristics of topological states, enabling…

Mesoscale and Nanoscale Physics · Physics 2016-08-03 Arun Bansil , Hsin Lin , Tanmoy Das

Topological electronic materials are new quantum states of matter hosting novel linear responses in the bulk and anomalous gapless states at the boundary, and are for scientific and applied reasons under intensive research in physics and in…

Materials Science · Physics 2019-03-01 Tiantian Zhang , Yi Jiang , Zhida Song , He Huang , Yuqing He , Zhong Fang , Hongming Weng , Chen Fang

The discoveries of intrinsically magnetic topological materials, including semimetals with a large anomalous Hall effect and axion insulators, have directed fundamental research in solid-state materials. Topological quantum chemistry has…

Topological states of matter, first discovered in quantum systems, have opened new avenues for wave manipulation beyond the quantum realm. In elastic media, realizing these topological effects requires identifying lattices that support the…

Materials Science · Physics 2025-03-24 Pegah Azizi , Rahul Dev Kundu , Weichen Li , Kai Sun , Xiaojia Shelly Zhang , Stefano Gonella

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…

Materials Science · Physics 2021-03-23 Nitesh Kumar , Satya N. Guin , Kaustuv Manna , Chandra Shekhar , Claudia Felser

We adapt the topological quantum chemistry formalism to layer groups, and apply it to study the band topology of 8,872 entries from the computational two-dimensional (2D) materials databases C2DB and MC2D. In our analysis, we find 4,073…

Mesoscale and Nanoscale Physics · Physics 2024-11-15 Urko Petralanda , Yi Jiang , B. Andrei Bernevig , Nicolas Regnault , Luis Elcoro

Recent discoveries of topological phases realized in electronic states in solids have revealed an important role of topology, which ubiquitously appears in various materials in nature. Many well-known materials have turned out to be…

Materials Science · Physics 2018-09-14 Motoaki Hirayama , Satoru Matsuishi , Hideo Hosono , Shuichi Murakami

Topological crystalline insulators (TCI) are insulating electronic phases of matter with nontrivial topology originating from crystalline symmetries. Recent theoretical advances have provided powerful guidelines to search for TCIs in real…

Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…

Mesoscale and Nanoscale Physics · Physics 2020-06-12 Hoi Chun Po

Topological metals are special conducting materials with gapless band structures and nontrivial edge-localized resonances, whose discovery has proved elusive because the traditional topological classification methods do not apply in this…

Mesoscale and Nanoscale Physics · Physics 2023-06-21 Wenting Cheng , Alexander Cerjan , Ssu-Ying Chen , Emil Prodan , Terry A. Loring , Camelia Prodan

Topological electronic flatten bands near or at the Fermi level are a promising avenue towards unconventional superconductivity and correlated insulating states. However, the related experiments are mostly limited to the engineered…

Topological phases, especially topological crystalline insulators (TCIs), have been intensively explored observed experimentally in three-dimensional (3D) materials. However, the two-dimensional (2D) films are explored much less than 3D…

Materials Science · Physics 2017-11-22 Yi-zhen Jia , Wei-xiao Ji , Chang-wen Zhang , Ping Li , Shu-feng Zhang , Pei-ji Wang , Sheng-shi Li , Shi-shen Yan
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