Related papers: Continuous Topological Insulators Classification a…
In this paper topological $K$-group calculations for fiber bundles with structure group $SO(3)$ over tori are carried out to explain why topological insulators have special conducting points on their surface but are bulk insulators. It is…
In topology, one averages over local geometrical details to reveal robust global features. This approach proves crucial for understanding quantized bulk transport and exotic boundary effects of linear wave propagation in (meta-)materials.…
A different type of topological phase dubbed topological inverse Anderson insulators is proposed, which is characterized by the disorder-induced extended bulk states from the flat-band localization and topological edge states. Based on the…
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…
We explore a large family of one-dimensional (1D) topological crystalline insulators (TCIs) classified by $\mathbb{Z}$ invariants protected by space-time inversion symmetry. This finding stands in marked contrast to the conventional…
We study topological phases in one-dimensional open Floquet systems driven by chiral symmetric nonunitary time evolution. We derive a procedure to calculate topological numbers from nonunitary time-evolution operators with chiral symmetry.…
Periodically-driven or Floquet systems can realize anomalous topological phenomena that do not exist in any equilibrium states of matter, whose classification and characterization require new theoretical ideas that are beyond the…
Several proposed applications and exotic effects in topological insulators rely on the presence of helical Dirac states at the interface between a topological and a normal insulator. In the present work, we have used low-energy…
Recently it was shown that the topological properties of $2D$ and $3D$ topological insulators are captured by a $\mathbb{Z}_2$ chiral anomaly in the boundary field theory. It remained, however, unclear whether the anomaly survives…
We argue that various kinds of topological insulators (TIs) can be insightfully characterized by an inspection of the charge centers of the hybrid Wannier functions, defined as the orbitals obtained by carrying out a Wannier transform on…
Very recently, increasing attention has been focused on non-Abelian topological charges, e.g. the quaternion group Q8. Different from Abelian topological band insulators, these systems involve multiple tangled bulk bandgaps and support…
Three novel applications of computational topology in the field of fusion science are developed. A procedure for the automatic classification of the orbits of magnetic field lines into topologically distinct classes using Vietoris-Rips…
Recent years have seen multiple high-throughput studies reveal an immense number of topological materials through use of symmetry indicators. Despite this success, three-dimensional topological insulators (TI) admitting a band-gap larger…
We study non-interacting electrons in disordered materials which exhibit a spectral gap, in each of the ten Altland--Zirnbauer symmetry classes, in all space dimensions. We define an appropriate space of Hamiltonians and a topology on it so…
This study presents an approach that leverages the existing knowledge acquired in one-dimensional BDI class discrete metamaterials, such as mass-spring systems or acoustic resonators, and exploits it to realize fully continuous elastic…
We focus on a scenario of non-Hermitian bulk--boundary correspondence that uses a topological invariant defined in a bulk geometry under a modified periodic boundary condition. Although this has succeeded in describing the topological…
Recent theories and experiments have suggested that strong spin-orbit coupling effects in certain band insulators can give rise to a new phase of quantum matter, the so-called topological insulator, which can show macroscopic entanglement…
For spinful systems with spin 1/2, it is generally believed that P and T invariant strong and second-order topologies exist in four band and eight band system, respectively. Here, by using periodic driving, we find it is possible to have…
The symmetry-based indicator [H. C. Po, A. Vishwanath, H. Watanabe, Nat. Commun. 8, 50 (2017)] is a practical tool to diagnose topological materials in the band theory. In this note, we present two directions to generalize the…
Topological insulators are characterized by specially protected conduction on their outer boundaries. We show that the protected edge conduction exhibited by 2-D topological insulators (and also Chern insulators) is independent of…