Related papers: $\mathbb{Z}_{2}$ Topological Index for Continuous …
Topological photonics has revolutionized our understanding of light propagation, but most of current studies are focused on designing a static photonic structure. Developing a dynamic photonic topological platform to switch multiple…
We describe how optical dressing can be used to generate bandstructures for ultracold atoms with non-trivial Z_2 topological order. Time reversal symmetry is preserved by simple conditions on the optical fields. We first show how to…
Topological insulators represent unique phases of matter with insulating bulk and conducting edge or surface states, immune to small perturbations such as backscattering due to disorder. This stems from their peculiar band structure, which…
Topological insulators are a new class of materials which have gapped spectra in the bulk, but are accompanied by topologically protected gapless excitations at the surface (edge) of the system. These phenomena have a close relationship…
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
Designing photonic topological insulators is highly non-trivial because it requires inversion of band symmetries around the band gap, which was so far done using intuition combined with meticulous trial and error. Here we take a completely…
We analyze generalizations of two dimensional topological insulators which can be realized in interacting, time reversal invariant electron systems. These states, which we call fractional topological insulators, contain excitations with…
We propose an interferometric method to measure Z2 topological invariants of time-reversal invariant topological insulators realized with optical lattices in two and three dimensions. We suggest two schemes which both rely on a combination…
We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…
Topological insulators (TIs) represent a novel quantum state of matter, characterized by edge or surface-states, showing up on the topological character of the bulk wave functions. Allowing electrons to move along their surface, but not…
The discovery of topological insulators has rapidly been followed by the advent of their photonic analogues, motivated by the prospect of backscattering-immune light propagation. So far, however, implementations have mainly relied on…
We discuss some aspects of topological invariants that classify topological states of matter with emphasis on topological insulators. The main aspect addressed is if there are only two topological phases to Bloch Hamiltonian that are time…
Topological classification in our previous paper [K. Shiozaki and M. Sato, Phys. Rev. B ${\bf 90}$, 165114 (2014)] is extended to nonsymmorphic crystalline insulators and superconductors. Using the twisted equivariant $K$-theory, we…
We study topological indices of Fermionic time-reversal invariant topological insulators in two dimensions, in the regime of strong Anderson localization. We devise a method to interpolate between certain Fredholm operators arising in the…
Many properties of photonic structures rely on band topology characterized by the integer invariants that can change during the topological transitions and give rise to the disorder-robust topological edge, corner, or interface states.…
Kondo insulators are particularly simple type of heavy electron material, where a filled band of heavy quasiparticles gives rise to a narrow band insulator. Starting with the Anderson lattice Hamiltonian, we develop a topological…
Topological insulators combine insulating properties in the bulk with scattering-free transport along edges, supporting dissipationless unidirectional energy and information flow even in the presence of defects and disorder. The feasibility…
Topological insulator materials have been extensively studied in the field of condensed matter physics because nontrivial topology in the electronic state gives rise to a novel spin-polarized Dirac dispersion on the surface. To describe the…
Electromagnetic waves propagating, at finite speeds, in conventional wave-guiding structures are reflected by discontinuities and decay in lossy regions. In this Letter, we drastically modify this typical guided-wave behavior by combining…
Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological…