Related papers: Topological electronic bands in crystalline solids

There are a variety of nonlinear optical effects including higher harmonic generations, photovoltaic effects, and nonlinear Kerr rotations. They are realized by the strong light irradiation to materials that results in nonlinear…

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…

We study topological properties of one-dimensional non-Hermitian systems without chiral symmetry and give phase diagrams characterized by topological invariants $\nu_E$ and $\nu_{total}$, associated with complex energy vorticity and…

In band theory of solids, degeneracies manifest themselves as point, line, and surface objects. The topological nature of band degeneracies has recently been appreciated since the recognition of gapless topological quantum phases of matter.…

Topological materials can host edge and corner states that are protected from disorder and material imperfections. In particular, the topological edge states of mechanical structures present unmatched opportunities for achieving robust…

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…

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 insulators (TCIs), and 3D topological semimetals…

Topology describes properties of physical systems that remain constant under continuous deformations. For infinite vector waves, global topological invariants in position space are typically associated with periodic patterns. We demonstrate…

A theory for nontrivial topology of band structure in metallic helimagnets is developed. Two theorems on electron dispersion in helimagnets are proved. They reveal a Kramers-like degeneracy in helical magnetic field. The generalized Bloch…

The interplay of topology and symmetry in a material's band structure may result in various patterns of topological states of different dimensionality on the boundary of a crystal. The protection of these "higher-order" boundary states…

Topological insulators have emerged as a major topic of condensed matter physics research with several novel applications proposed. Although there are now a number of established experimental examples of materials in this class, all of them…

A fundamental open problem in condensed matter physics is how the dichotomy between conventional and topological band insulators is modified in the presence of strong electron interactions. We show that there are 6 new electronic…

Among different topological and related phases of condensed matter, nodal semimetals occupy a special place - the electronic band topology in these materials is related to three-dimensional bulk, rather than to surface, states. A great…

Crystalline semimetals with certain space group symmetries may possess unusual electronic structure topology, distinct from the conventional Weyl and Dirac semimetals. Characteristic property of these materials is the existence of…

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…

In photonics, band degeneracies at high-symmetry points in wavevector space have been shown to exhibit rich physical phenomena. However, obtaining degenerate bands away from such points is highly nontrivial. In this work, we achieve complex…

The study of band topology in photonic crystals was primarily focused on near-field effects, including edge states and high order corner states. However, this work investigated the polarization distribution of radiated fields for photonic…

The discovery of topological insulators and semimetals has opened up a new perspective to understand materials. Owing to the special band structure and enlarged Berry curvature, the linear responses are strongly enhanced in topological…

Topological phases of matter are often understood and predicted with the help of crystal symmetries, although they don't rely on them to exist. In this chapter we review how topological phases have been recently shown to emerge in amorphous…

The electronic band structure, describing the periodic dependence of electronic quantum states on lattice momentum in reciprocal space, is a fundamental concept in solid-state physics. However, it's only well-defined for static nuclei. To…