Related papers: Resolving the Topological Classification of Bismut…

Topological materials are defined by the correspondence between bulk topology and boundary states, yet this correspondence becomes enigmatic on low-symmetry surfaces where bulk and surface periodicities are inherently mismatched. Here we…

Tessellations of the hyperbolic spaces by regular polygons are becoming popular because they support discrete quantum and classical models displaying unique spectral and topological characteristics. Resolving the true bulk spectra and the…

To clarify the relationship between edge electronic states in open-boundary crystalline systems and their corresponding bulk electronic structure, Alase et al. [Phys. Rev. Lett. 117, 076804 (2016)] have recently generalized Bloch's theorem…

We show that lattices with higher-order topology can support corner-localized bound states in the continuum (BICs). We propose a method for the direct identification of BICs in condensed matter settings and use it to demonstrate the…

The paradigm of classifying three-dimensional (3D) topological insulators into strong and weak ones (STI and WTI) opens the door for the discovery of various topological phases of matter protected by different symmetries and defined in…

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…

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…

Electronic bands featuring nontrivial bulk topological invariant manifest through robust gapless modes at the boundaries, e.g., edges and surfaces. As such this bulk-boundary correspondence is also operative in driven quantum materials. For…

We dedicate this paper to the topological analysis of subwavelength solutions in Floquet metamaterials. This work should be considered as a basis for further investigation on whether topological properties of the bulk materials are linked…

This paper reviews recent results on the classification of partial differential operators modeling bulk and interface topological insulators in Euclidean spaces. Our main objective is the mathematical analysis of the unusual,…

The discovery of topological phases has ushered in a new era of condensed matter physics and revealed a variety of natural and artificial materials. They obey the bulk-boundary correspondence (BBC), which guarantees the emergence of…

Unlike the edge state of a topological insulator where its energy level lives in the bulk energy gap, the edge state of a topological semimetal hides in the bulk spectrum and is difficult to be identified by the energy. We investigate the…

Setting the cosmological constant to be dynamical, we study the bulk and boundary thermodynamics of charged Anti-de Sitter black holes. We develop mass/energy formulas in terms of thermodynamic state functions for the extended…

We study the bulk and boundary properties of fragile topological insulators (TIs) protected by inversion symmetry, mostly focusing on the class A of the Altland-Zirnbauer classification. First, we propose an efficient method for diagnosing…

A generalized disclination (g.disclination) theory [AF15] has been recently introduced that goes beyond treating standard translational and rotational Volterra defects in a continuously distributed defects approach; it is capable of…

The topology of insulators is usually revealed through the presence of gapless boundary modes: this is the so-called bulk-boundary correspondence. However, the many-body wavefunction of a crystalline insulator is endowed with additional…

Bulk boundary correspondence is crucial to topological insulator as it associates the boundary states (with zero energy, chiral or helical) to topological numbers defined in bulk. The application of this correspondence needs a prerequisite…

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…

Topological insulating phases are usually found in periodic lattices stemming from collective resonant effects, and it may thus be expected that similar features may be prohibited in thermal diffusion, given its purely dissipative and…

Finite topologically non-trivial systems are often characterised by the presence of bound states at their physical edges. These topological edge modes can be distinguished from usual Shockley waves energetically, as their energies remain…