Related papers: Bloch classification surface for three-band system…
Bloch theory describes the electronic states in crystals whose energies are distributed as bands over the Brillouin zone. The electronic states corresponding to a (few) isolated energy band(s) thus constitute a vector bundle. The…
We show that flat bands can be categorized into two distinct classes, that is, singular and nonsingular flat bands, by exploiting the singular behavior of their Bloch wave functions in momentum space. In the case of a singular flat band,…
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…
A Bloch sphere is the geometrical representation of an arbitrary two-dimensional Hilbert space. Possible classes of entanglement and separability for the pure and mixed states on the Bloch sphere were suggested by [M. Boyer, R. Liss, T.…
Topological properties of energy spectra of general one-dimensional quasiperiodic systems, describing also Bloch electrons in magnetic fields, are studied for an infinity of irrational modulation frequencies corresponding to irrational…
We review recent progresses in the study of flat band systems, especially focusing on the fundamental physics related to the singularity of the flat band's Bloch wave functions. We first explain that the flat bands can be classified into…
Topology and geometry are essential to our understanding of modern physics, underlying many foundational concepts from high energy theories, quantum information, and condensed matter physics. In condensed matter systems, a wide range of…
An exact analytical expression is derived for Bloch states in three dimensions, based on the only assumption that the electronic wavefunction can be expanded in terms of Gaussian type orbitals. The resulting expression features…
Previous studies have shown that the bulk topology of single-particle systems can be captured by the band inversion surface or by the spin inversion surface emerged on the time-averaged spin polarization. Most of the studies, however, are…
Band structure analysis is central to understanding wave propagation in periodic media; however, it becomes challenging in open systems owing to energy leakage. Photonic crystal (PhC) slabs exemplify such systems, featuring periodicity in…
Electronic bands in crystals are described by an ensemble of Bloch wave functions indexed by momenta defined in the first Brillouin Zone, and their associated energies. In an insulator, an energy gap around the chemical potential separates…
Non-Hermitian quantum systems can exhibit unique observables characterizing topologically protected transport in the presence of decay. The topological protection arises from winding numbers associated with non-decaying dark states, which…
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…
Conventionally, symmetry-protected topological phases and band crossings are protected by global symmetries acting on the entire system. Here, we show that symmetries preserved only on a partial region of a system, termed local support…
Entanglement is an important concept in quantum information, quantum communication, and quantum computing. We provide a geometrical analysis of entanglement and separability for all the rank-2 quantum mixed states: complete analysis for the…
Electronic band structure for electrons bound on periodic minimal surfaces is differential-geometrically formulated and numerically calculated. We focus on minimal surfaces because they are not only mathematically elegant (with the surface…
We classify combinations of isolated singularities that can occur on complex cubic threefolds generalizing analogous results for cubic surfaces due to Schl\"{a}fli and Bruce--Wall. In addition, we provide concise combinatorial description…
We report new oscillations of wavepackets in quantum walks subjected to electric fields, that decorate the usual Bloch-Zener oscillations of insulators. The number of turning points (or sub-oscillations) within one Bloch period of these…
Band topology has been studied as a design principle of realizing robust boundary modes. Here, by exploring non-Hermitian topology, we propose a three-dimensional topological laser that amplifies surface modes. The topological surface laser…
Three dimensional topological insulators are bulk insulators with $\mathbf{Z}_2$ topological electronic order that gives rise to conducting light-like surface states. These surface electrons are exceptionally resistant to localization by…