相关论文: Homotopic classification of band structures: Stabl…

We proposed a framework for the topological classification of non-Hermitian systems. Different from previous $K$-theoretical approaches, our approach is a homotopy classification, which enables us to see more topological invariants.…

The moire flat bands in twisted bilayer graphene have attracted considerable attention not only because of the emergence of correlated phases but also due to their nontrivial topology. Specifically, they exhibit a new class of topology that…

One of the hallmarks of topological insulators is the correspondence between the value of its bulk topological invariant and the number of topologically protected edge modes observed in a finite-sized sample. This bulk-boundary…

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…

Stable homotopy theory is governed by the principle that after inverting loop spaces, homotopy types become the representing objects for homology theories. We show that this principle extends to higher category theory: inverting…

In the research of the topological band phases, the conventional wisdom is to start from the crystalline translational symmetry systems. Nevertheless, the translational symmetry is not always a necessary condition for the energy bands. Here…

We revisit the problem of classifying topological band structures in non-Hermitian systems. Recently, a solution has been proposed, which is based on redefining the notion of energy band gap in two different ways, leading to the so-called…

Topological phases in electronic structures contain a new type of topology, called fragile, which can arise, for example, when an Elementary Band Representation (Atomic Limit Band) splits into a particular set of bands. We obtain, for the…

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, such as Chern insulators, are defined in terms of additive indices that are stable against the addition of trivial degrees of freedom. Such topology presents an obstruction to any Wannier representation, namely, the…

The geometric properties of a lattice can have profound consequences on its band spectrum. For example, symmetry constraints and geometric frustration can give rise to topologicially nontrivial and dispersionless bands, respectively.…

The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to…

The interplay of topology and symmetry in a material's band structure may result in various patterns of topological states of different dimensionality on the boundary of a crystal. The protection of these "higher-order" boundary states…

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"…

Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path towards coherent spin transport for spintronics applications.…

Band topology is both constrained and enriched by the presence of symmetry. The importance of anti-unitary symmetries such as time reversal was recognized early on leading to the classification of topological band structures based on the…

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…

Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of…

Symmetries crucially underlie the classification of topological phases of matter. Most materials, both natural as well as architectured, possess crystalline symmetries. Recent theoretical works unveiled that these crystalline symmetries can…

Graph classification plays an important role is data mining, and various methods have been developed recently for classifying graphs. In this paper, we propose a novel method for graph classification that is based on homotopy equivalence of…