Topological quantum chemistry

  title={Topological quantum chemistry},
  author={Barry Bradlyn and Luis Elcoro and Jennifer Cano and Maia G. Vergniory and Zhijun Wang and Claudia Felser and Mois I Aroyo and Bogdan Andrei Bernevig},
Since the discovery of topological insulators and semimetals, there has been much research into predicting and experimentally discovering distinct classes of these materials, in which the topology of electronic states leads to robust surface states and electromagnetic responses. This apparent success, however, masks a fundamental shortcoming: topological insulators represent only a few hundred of the 200,000 stoichiometric compounds in material databases. However, it is unclear whether this low… 

Towards a topological quantum chemistry description of correlated systems: The case of the Hubbard diamond chain

: The recently introduced topological quantum chemistry (TQC) framework has provided a description of universal topological properties of all possible band insulators in all space groups based on

Topological Quantum Materials from the Viewpoint of Chemistry

This review presents the topological concepts related to solids from the viewpoint of a solid-state chemist, summarizes techniques for growing single crystals, and describes basic physical property measurement techniques to characterize topological materials beyond their structure and provide examples of such materials.

Efficient topological materials discovery using symmetry indicators

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

A chemical theory of topological insulators.

Research on topological insulators (TIs) has experienced an exponential growth in the last few years, promising new technological applications in fields ranging from electronics to quantum computing.

Topological materials discovery from crystal symmetry

Topological materials discovery has evolved at a rapid pace over the past 15 years following the identification of the first nonmagnetic topological insulators (TIs), topological crystalline

All topological bands of all nonmagnetic stoichiometric materials

Topological quantum chemistry and symmetry-based indicators have facilitated large-scale searches for materials with topological properties at the Fermi energy (EF). We report the implementation of a

The topology of electronic band structures

This Perspective provides a broad introduction to topological phases, their known properties, and material realizations, with a particular focus on semimetals, and highlights areas where the field can continue to make remarkable discoveries.

Chemical Principles of Topological Semimetals

Initiated by the discovery of topological insulators, topologically non-trivial materials have attracted immense interest in the physics community in the past decade. One of the latest additions to

Band structure engineering in 3D topological insulators

  • L. Plucinski
  • Physics
    Journal of physics. Condensed matter : an Institute of Physics journal
  • 2019
This review presents theoretical concepts and a selection of experimental results from the point view of a spectroscopist, and might be useful for physicists who want to get familiar with the key concepts in a self-contained form with formalism reduced to readily understandable concepts.

Topological semimetal driven by strong correlations and crystalline symmetry

Electron correlations amplify quantum fluctuations and, as such, are recognized as the origin of many quantum phases. However, whether strong correlations can lead to gapless topological states is an



Graph theory data for topological quantum chemistry.

This paper provides the explicit data and formulate the necessary algorithms to produce all topologically distinct graphs and shows how to apply these algorithms to certain "elementary" band structures highlighted in the reference, and thus identified and tabulated all orbital types and lattices that can give rise to topologically disconnected band structures.

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

The authors present a framework for identifying topologically distinct band-structures for all 3D space groups by developing an efficient way to represent band structures in terms of elementary basis states, and isolating the topological ones by removing the subset of atomic insulators.

Discovery of a Three-Dimensional Topological Dirac Semimetal, Na3Bi

Na3Bi is established as a model system for 3D TDSs, which can serve as an ideal platform for the systematic study of quantum phase transitions between rich topological quantum states, and the robustness of 3D Dirac fermions in Na3Bi against in situ surface doping is demonstrated.

Topological Classification of Crystalline Insulators through Band Structure Combinatorics

We present a method for efficiently enumerating all allowed, topologically distinct, electronic band structures within a given crystal structure in all physically relevant dimensions. The algorithm

A stable three-dimensional topological Dirac semimetal Cd3As2.

By performing angle-resolved photoemission spectroscopy, a pair of 3D Dirac fermions in Cd3As2 are directly observed, proving that it is a model 3D TDS and by in situ doping it is able to tune its Fermi energy, making it a flexible platform for exploring exotic physical phenomena.

Quantized electric multipole insulators

This work introduces a paradigm in which “nested” Wilson loops give rise to topological invariants that have been overlooked and opens a venue for the expansion of the classification of topological phases of matter.

Observation of a large-gap topological-insulator class with a single Dirac cone on the surface

Recent experiments and theories have suggested that strong spin–orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator,

Two-dimensional oxide topological insulator with iron-pnictide superconductor LiFeAs structure

By using first-principles calculations, we propose that ZrSiO can be looked at as a three-dimensional (3D) oxide weak topological insulator (TI) and its single layer is a long-sought-after 2D oxide

Direct measurement of the Zak phase in topological Bloch bands

Geometric phases that characterize the topological properties of Bloch bands play a fundamental role in the band theory of solids. Here we report on the measurement of the geometric phase acquired by

Emergence of topological bands on the surface of ZrSnTe crystal

By using angle-resolved photoemission spectroscopy combined with first-principles calculations, we reveal that the topmost unit cell of ZrSnTe crystal hosts two-dimensional (2D) electronic bands of