Related papers: Topological electronic bands in crystalline solids
Topological properties lie at the heart of many fascinating phenomena in solid state systems such as quantum Hall systems or Chern insulators. The topology can be captured by the distribution of Berry curvature, which describes the geometry…
In recent years, there have been rapid advances in the parallel fields of electronic and photonic topological crystals. Topological photonic crystals in particular show promise for coherent transport of light and quantum information at…
Recent experiments on multilayer graphene systems have rekindled interest in electronic crystal phases in two dimensions -- but now for phases enriched by non-trivial quantum geometry. In this work, we introduce a simple continuum model…
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…
In 2+1D, topological electromagnetic phases are defined as atomic-scale media which host photonic monopoles in the bulk band structure and respect bosonic symmetries. Additionally, they support topologically protected spin-1 edge states,…
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 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 article, we provide a pedagogical review of the theory of topological quantum chemistry and topological crystalline insulators. We begin with an overview of the properties of crystal symmetry groups in position and momentum space.…
We develop a unified view of topological phase transitions (TPTs) in solids by revising the classical band theory with the inclusion of topology. Re-evaluating the band evolution from an "atomic crystal" [a normal insulator (NI)] to a solid…
The conventional theory of solids is well suited to describing band structures locally near isolated points in momentum space, but struggles to capture the full, global picture necessary for understanding topological phenomena. In part of a…
We develop the topological band theory for systems described by non-Hermitian Hamiltonians, whose energy spectra are generally complex. After generalizing the notion of gapped band structures to the non-Hermitian case, we classify "gapped"…
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to…
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…
The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material…
Recent discoveries of topological phases realized in electronic states in solids have revealed an important role of topology, which ubiquitously appears in various materials in nature. Many well-known materials have turned out to be…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
Topological phases play a crucial role in the fundamental physics of light-matter interaction and emerging applications of quantum technologies. However, the topological band theory of waveguide QED systems is known to break down, because…
Topological materials hosting multifold fermions and bosons have emerged as a rich platform for exploring unconventional quasiparticles and transport phenomena. In this work, we investigate the chiral crystal SiTc using first-principles…
Nodal lines inside the momentum space of three-dimensional crystalline solids are topologically stabilized by a $\pi$-flux of Berry phase. Nodal-line rings in $\mathcal{PT}$-symmetric systems with negligible spin-orbit coupling (here…
Despite the extensive studies of topological states, their characterization in strongly nonlinear classical systems has been lacking. In this work, we identify the proper definition of Berry phase for nonlinear bulk modes and characterize…