Related papers: Topological quantum chemistry
Our understanding of topological insulators is based on an underlying crystalline lattice where the local electronic degrees of freedom at different sites hybridize with each other in ways that produce nontrivial band topology, and the…
We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological…
One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…
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…
It is known that any covering space of a topological group has the natural structure of a topological group. This article discusses a noncommutative generalization of this fact. A noncommutative generalization of the topological group is a…
We show that certain band gaps, which appear topologically trivial from the perspective of symmetry indicators (SIs), must instead be topological, as guaranteed by real-space information that follows from Topological Quantum Chemistry…
Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path towards coherent spin transport for spintronics applications.…
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…
A topological superconductor, characterized by either a chiral order parameter or a chiral topological surface state in proximity to bulk superconductivity, is foundational to topological quantum computing. As in other topological phases of…
On the basis of the "molecular-orbital" representation which describes generic flat-band models, we propose a systematic way to construct a class of flat-band models with finite-range hoppings that have topological natures. In these models,…
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 topological insulator (TI) state, though…
The electronic bands are classified according to their topology. We compute the connection and curvature for the electronic bands and show that the physical properties are determined by topological invariants which are equivalent to the…
In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…
Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…
The topological classification of all known non-magnetic crystalline compounds is now complete, revealing thousands of new candidate topological materials waiting to be explored in the lab.
The "chemical bond" is a central concept in molecular sciences, but there is no consensus as to what a bond actually is. Therefore, a variety of bonding models have been developed, each defining the structure of molecules in a different…
The recent discovery of topological insulator (TI) offers new opportunities for the development of thermoelectrics, because many TIs (like Bi$_2$Te$_3$) are excellent thermoelectric (TE) materials. In this review, we will first describe the…
Topological semimetals, such as the Weyl and Dirac semimetals, represent one of the most active research fields in modern condensed matter physics. The peculiar physical properties of these systems mainly originate from their underlying…
Topological photonics provides a powerful framework to describe and understand many nontrivial wave phenomena in complex electromagnetic platforms. The topological index of a physical system is an abstract global property that depends on…
We show that compositions of time-reversal and spatial symmetries, also known as the magnetic-space-group symmetries, protect topological invariants as well as surface states that are distinct from those of all preceding topological states.…