相关论文: Extended topological group structure due to averag…

We discuss topology in dissipative quantum systems from the perspective of quantum trajectories. The latter emerge in the unraveling of Markovian quantum master equations and/or in continuous quantum measurements. Ensemble-averaging quantum…

This paper explores the cohomology of linear cycle sets, focusing on extensions of a specific linear cycle set H by an abelian group I. We derive explicit formulas for the second cohomology group, which classifies these extensions, and…

In this article it is proved that the dynamical properties of a broad class of semilinear parabolic problems are sensitive to arbitrarily small but smooth perturbations of the nonlinear term, when the spatial dimension is either equal to…

The effect of surface disorder on electronic systems is particularly interesting for topological phases with surface and edge states. Using exact diagonalization, it has been demonstrated that the surface states of a 3D topological…

In order for non-Hermitian (NH) topological effects to be relevant for practical applications, it is necessary to study disordered systems. In the absence of disorder, certain driven-dissipative cavity arrays with engineered non-local…

Topological phenomena are commonly studied in phases of matter which are separated from a trivial phase by an unavoidable quantum phase transition. This can be overly restrictive, leaving out scenarios of practical relevance -- similar to…

We present a method for computing the classification groups of topological insulators and superconductors in the presence of $\mathbb{Z}_2^{\times n}$ point group symmetries, for arbitrary natural numbers $n$. Each symmetry class is…

We construct fixed-point wave functions and exactly solvable commuting-projector Hamiltonians for a large class of bosonic symmetry-enriched topological (SET) phases, based on the concept of equivalent classes of symmetric local unitary…

Photonic topological insulators exhibit bulk-boundary correspondence, which requires that boundary-localized states appear at the interface formed between topologically distinct insulating materials. However, many topological photonic…

We develop a theory of topological transitions in a Floquet topological insulator, using graphene irradiated by circularly polarized light as a concrete realization. We demonstrate that a hallmark signature of such transitions in a static…

This paper demonstrates the existence of topological models with gapped edge states but protected extended bulk states against disorder. Such systems will be labeled as trivial by the current classification of topological insulators. Our…

In this work, we present a generalization of extended persistent homology to filtrations of graded sub-groups by defining relative homology in this setting. Our work provides a more comprehensive and flexible approach to get an algebraic…

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…

Topological insulators are characterized by insulating bulk and conducting surface, the latter is a necessity consequence of the nontrivial topology of the wavefunctions forming the valence band. This chapter gives a historical overview of…

The theory of topological insulators and superconductors has mostly focused on non-interacting and gapped systems. This review article discusses topological phases that are either gapless or interacting. We discuss recent progress in…

Topological objects can influence each other if the underlying homotopy groups are non-Abelian. Under such circumstances, the topological charge of each individual object is no longer a conserved quantity and can be transformed to each…

We use the method of bulk-boundary correspondence of topological invariants to show that disordered topological insulators have at least one delocalized state at their boundary at zero energy. Those insulators which do not have chiral…

This work addresses the existence of transitive extensions of certain infinite permutation groups which arise as the automorphism groups of model-theoretic structures which are generic in the Fra\"iss\'e sense. The study of transitive…

An exhaustive classification scheme of topological insulators and superconductors is presented. The key property of topological insulators (superconductors) is the appearance of gapless degrees of freedom at the interface/boundary between a…

Excitonic insulator remains elusive and there has been a lack of reliable identification methods. In this work, we demonstrate the promise of topological excitonic insulators for identification due to their unique bulk-edge correspondence,…