Related papers: Local markers for crystalline topology

The interplay between symmetry and topology leads to a rich variety of electronic topological phases, protecting states such as the topological insulators and Dirac semimetals. Previous results, like the Fu-Kane parity criterion for…

Topological crystalline phases in electronic structures can be generally classified using the spatial symmetry characters of the valence bands and mapping them onto appropriate symmetry indicators. These mappings have been recently applied…

Photonic structures with topologically nontrivial bands are usually designed by arranging simple meta-atoms, ideally, single-mode ones, in a carefully designed photonic lattice with symmetry that guarantees the emergence of topological…

The systematic diagnosis of band topology enabled by the method of "symmetry indicators" underlies the recent advances in the search for new materials realizing topological crystalline insulators. Such an efficient method has been missing…

Though symmetry-based indicators formulae are powerful in diagnosing topological states with a gapped band structure at/between any high-symmetry points, it fails in diagnosing topological degeneracies when the compatibility condition is…

Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators…

Topological invariants have proved useful for analyzing emergent function as they characterize a property of the entire system, and are insensitive to local details, disorder, and noise. They support boundary states, which reduce the system…

Nonlocal crystals are systems with translational symmetry but arbitrary range couplings or interactions between degrees of freedom. We argue that the notion of topology in such systems does not collapse to that in zero dimensions, as one…

One of the principal goals in the design of photonic crystals is the engineering of band gaps and defect states. Drawing on the concepts of band-structure topology, I here describe the formation of exponentially localized, topologically…

The introduction of topology unravels a new chapter of physics. Topological systems provide unique edge/interfacial quantum states which are expected to contribute to the development of novel spintronics and open the door to robust quantum…

There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…

Topological materials are quantum materials with nontrivial ground-state entanglement that are irremovable so long as certain rules, like invariance under symmetries and the existence of an energy gap, are respected. They showcase…

Topological insulators are described by topological invariants that can be computed by integrals over momentum space, but also as traces over local, real-space topological markers. These markers are useful to detect topological insulating…

The fundamental, or first, band gap is of unmatched importance in the study of photonic crystals. Here, we address precisely where this gap can be opened in the band structure of three-dimensional photonic crystals. Although strongly…

Topological phase transitions, characterized by the closing and reopening of band gaps and a concomitant change in topological invariants, have played a central role in topological physics. However, such transitions have so far been…

Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery…

Since topological insulators were theoretically predicted and experimentally observed in semiconductors with strong spin-orbit coupling, more and more attention has been drawn to topological materials which host exotic surface states. These…

Rapidly growing demands for fast information processing have launched a race for creating compact and highly efficient optical devices that can reliably transmit signals without losses. Recently discovered topological phases of light…

We analyze the robustness of corner modes in topological photonic crystals, taking a $C_6$-symmetric breathing honeycomb photonic crystal as an example. First, we employ topological quantum chemistry and Wilson loop calculations to…

Topological photonics has received extensive attention from researchers because it provides brand new physical principles to manipulate light. Band topology of optical materials is characterized using the Berry phase defined by Bloch…