Related papers: Band Representations and Topological Quantum Chemi…
Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond…
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.…
We give an introduction to topological crystalline insulators, that is, gapped ground states of quantum matter that are not adiabatically connected to an atomic limit without breaking symmetries that include spatial transformations, like…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
Traditional ionic/covalent compound insulators arise from a commensuration between electron count and system volume. On the other hand, conventional topological insulators, outside of quantum hall effect systems, do not typically display…
There have been significant recent advances in realizing bandstructures with geometrical and topological features in experiments on cold atomic gases. We provide an overview of these developments, beginning with a summary of the key…
Topological phases, such as Chern insulators, are defined in terms of additive indices that are stable against the addition of trivial degrees of freedom. Such topology presents an obstruction to any Wannier representation, namely, the…
Topological photonics provides a robust and flexible platform for controlling light, enabling functionalities such as backscattering-immune edge transport and slow-light propagation. In this work, we design and characterize photonic…
Topological semimetals have emerged as an important class of quantum materials with novel electronic responses and unconventional transport phenomena. Among them, nodal-line semimetals are distinguished by band crossings that extend along…
In this paper, we introduce and study representation homology of topological spaces, which is a natural homological extension of representation varieties of fundamental groups. We give an elementary construction of representation homology…
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…
Topological photonic crystals, which offer topologically protected and back-scattering-immune transport channels, have recently gained significant attention for both scientific and practical reasons. Although most current studies focus on…
The fundamental building blocks in band theory are band representations (BRs): bands whose infinitely-numbered Wannier functions are generated (by action of a space group) from a finite number of symmetric Wannier functions centered on a…
One-dimensional crystals serve as a versatile platform for engineering nontrivial states, which can be easily explored in transport configurations. In this work, we analyze the properties of a periodic structure composed of an H-shaped unit…
"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…
A number of recent articles have reported the existence of topologically non-trivial states and associated end states in one-dimensional incommensurate lattice models that would usually only be expected in higher dimensions. Using an…
In this work, we introduce {\em topological representations of a quiver} as a system consisting of topological spaces and its relationships determined by the quiver. Such a setting gives a natural connection between topological…
Symmetry groups are projectively represented in quantum mechanics, and crystalline symmetries are fundamental in condensed matter physics. Here, we systematically present a unified theory of quantum mechanical space groups from two…
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…
We consider the extent to which symmetry eigenvalues reveal the topological character of bands. Specifically, we compare distinct atomic limit phases (band representations) that share the same irreducible representations (irreps) at all…