Related papers: Band Representations and Topological Quantum Chemi…

Discoveries of topological states and topological materials reshape our understanding of physics and materials over the last 15 years. First-principles calculations have been playing a significant role in bridging the theory of topology and…

We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by…

Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…

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…

This paper is an introduction to diagrammatic methods for representing quantum processes and quantum computing. We review basic notions for quantum information and quantum computing. We discuss topological diagrams and some issues about…

Photonic crystals (PhCs) have emerged as a popular platform for realizing various topological phases due to their flexibility and potential for device applications. In this article, we present a comprehensive classification of topological…

For a long time, band theory of solids has focused on the energy spectrum, or Hamiltonian eigenvalues. Recently, it was realized that the collection of eigenvectors also contains important physical information. The local geometry of…

Madsen et al. [arXiv:1307.2577] claim that one-dimensional insulating crystals and one-dimensional insulating quasicrystals are topologically equivalent and, thus, trivial. In this comment, we clarify that in topological classification of…

We propose a concrete application of the Atiyah-Singer index formula in molecular physics, giving the exact number of levels in energy bands, in terms of vector bundles topology. The formation of topologically coupled bands is demonstrated.…

In this review, we discuss recent progress in the explorations of topological materials beyond topological insulators; specifically, we focus on topological crystalline insulators and bulk topological superconductors. The basic concepts,…

We analyze the symmetry and topological features of a family of materials closely related to penta-graphene, derived from it by adsorption or substitution of different atoms. Our description is based on a novel approach, called topological…

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…

Topological phases of matter have sparked an immense amount of activity in recent decades. Topological materials are classified by topological invariants that act as a non-local order parameter for any symmetry and condition. As a result,…

Topological insulators and their intriguing edge states can be understood in a single-particle picture and can as such be exhaustively classified. Interactions significantly complicate this picture and can lead to entirely new insulating…

Electronic bands in crystals are described by an ensemble of Bloch wave functions indexed by momenta defined in the first Brillouin Zone, and their associated energies. In an insulator, an energy gap around the chemical potential separates…

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can…

Bloch theory describes the electronic states in crystals whose energies are distributed as bands over the Brillouin zone. The electronic states corresponding to a (few) isolated energy band(s) thus constitute a vector bundle. The…

We study the vibrational spectrum of a constrained classical ring. Due to the presence of 2-order exceptional points, a topologically trivial band at the infinity can make the vibrational band topologically nontrivial. The symmetry, which…

Band insulators appear in a crystalline system only when the filling -- the number of electrons per unit cell and spin projection -- is an integer. At fractional filling, an insulating phase that preserves all symmetries is a Mott…

Topological photonic crystals have received considerable attention for their ability to manipulate and guide light in unique ways. They are typically designed by hand based on careful analysis of their bands and mode profiles, but recent…