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In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…

Mesoscale and Nanoscale Physics · Physics 2015-02-17 M. Zahid Hasan , Su-Yang Xu , Madhab Neupane

Proposing new materials by atom substitution based on periodic table similarity is a conventional strategy of searching for materials with desired property. We introduce a machine learning frame work that promotes this paradigm to be…

Materials Science · Physics 2019-04-19 Lei Gu , Ruqian Wu

Topologically ordered phases of matter elude Landau's symmetry-breaking theory, featuring a variety of intriguing properties such as long-range entanglement and intrinsic robustness against local perturbations. Their extension to…

Persistent homology is a powerful tool for characterizing the topology of a data set at various geometric scales. When applied to the description of molecular structures, persistent homology can capture the multiscale geometric features and…

Quantitative Methods · Quantitative Biology 2018-07-31 Zixuan Cang , Guo-Wei Wei

Topological quantum materials have emerged as a frontier in condensed matter physics as well as in materials science, with intriguing electronic states that are robust to perturbations. Among the diverse structural motifs, kagome, chiral,…

Accurate prediction of molecular properties in complex chemical systems is crucial for accelerating material discovery and chemical innovation. However, current computational methods often struggle to capture the intricate compositional…

Chemical Physics · Physics 2025-09-24 Jinming Fan , Chao Qian , Shaodong Zhou

Machine learning (ML) has seen promising developments in materials science, yet its efficacy largely depends on detailed crystal structural data, which are often complex and hard to obtain, limiting their applicability in real-world…

Materials Science · Physics 2024-12-10 Namkyeong Lee , Heewoong Noh , Gyoung S. Na , Jimeng Sun , Tianfan Fu , Marinka Zitnik , Chanyoung Park

In this Perspective article, we explore some of the promising spin and topology material platforms (e.g. spins in semi- and superconductors, skyrmionic, topological and 2D materials) being developed for such quantum components as qubits,…

Conventional metals, insulators, and semimetals are constrained by fundamental limitations in terms of their thermoelectric performance. Topological materials offer certain features that allow them to circumvent these constraints, and…

Materials Science · Physics 2026-03-26 Brian Skinner , Poulomi Chakraborty , Joshua Scales , Joseph P. Heremans

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure. The algorithm applies to crystals with broken time-reversal, particle-hole, and chiral…

Mesoscale and Nanoscale Physics · Physics 2017-12-27 Jorrit Kruthoff , Jan de Boer , Jasper van Wezel , Charles L. Kane , Robert-Jan Slager

The tenfold classification provides a powerful framework for organizing topological phases of matter based on symmetry and spatial dimension. However, it does not offer a systematic method for transitioning between classes or engineering…

Mesoscale and Nanoscale Physics · Physics 2025-08-08 Amit Goft , Eric Akkermans

Modern quantum chemistry can make quantitative predictions on an immense array of chemical systems. However, the interpretation of those predictions is often complicated by the complex wave function expansions used. Here we show that an…

Chemical Physics · Physics 2013-11-12 Gerald Knizia

Robustness against small perturbations is a crucial feature of topological properties. This robustness is both a source of theoretical interest and a drive for technological applications, but presents a challenge when looking for new…

Mesoscale and Nanoscale Physics · Physics 2021-01-04 Cyrill Bösch , Tena Dubček , Frank Schindler , Andreas Fichtner , Marc Serra-Garcia

Phenomenological rules play a central role in the design of chemical reactions and materials with targeted properties. Typically, these are formulated heuristically in terms of non-interacting orbitals and bands, yet show remarkable…

Strongly Correlated Electrons · Physics 2026-02-20 Carlos Mejuto-Zaera , Michele Fabrizio

Even though thermodynamic energy-based crystal structure prediction (CSP) has revolutionized materials discovery, the energy-driven CSP approaches often struggle to identify experimentally realizable metastable materials synthesized through…

Materials Science · Physics 2025-05-15 Yu Xin , Peng Liu , Zhuohang Xie , Wenhui Mi , Pengyue Gao , Hong Jian Zhao , Jian Lv , Yanchao Wang , Yanming Ma

Despite the success of deep learning methods in quantum chemistry, their representational capacity is most often confined to neutral, closed-shell molecules. However, real-world chemical systems often exhibit complex characteristics,…

The prediction of material structure from chemical composition has been a long-standing challenge in natural science. Although there have been various methodological developments and successes with computer simulations, the prediction of…

Materials Science · Physics 2018-05-23 Naoto Tsujimoto , Daiki Adachi , Ryosuke Akashi , Synge Todo , Shinji Tsuneyuki

Topological quantum chemistry (TQC) is a successful framework for identifying (noninteracting) topological materials. Based on the symmetry eigenvalues of Bloch eigenstates at maximal momenta, which are attainable from first principles…

Topology has emerged as a fundamental property of many systems, manifesting in cosmology, condensed matter, high-energy physics and waves. Despite the rich textures, the topology has largely been limited to low dimensional systems that can…

Quantum Physics · Physics 2025-03-18 Robert de Mello Koch , Pedro Ornelas , Neelan Gounden , Bo-Qiang Lu , Isaac Nape , Andrew Forbes

For closed quantum systems, topological orders are understood through the equivalence classes of ground states of gapped local Hamiltonians. The generalization of this conceptual paradigm to open quantum systems, however, remains elusive,…

Strongly Correlated Electrons · Physics 2025-10-10 Tai-Hsuan Yang , Bowen Shi , Jong Yeon Lee