Related papers: Non-Commutative Tools for Topological Insulators
Topological insulators are new class of materials which are characterized by a bulk band gap like ordinary band insulator but have protected conducting states on their edge or surface. These states emerge out due to the combination of…
The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of…
Higher-order topological insulators (HOTI) are a novel topological phase beyond the framework of the conventional bulk-boundary correspondence. In these peculiar systems, the topologically nontrivial boundary modes are characterized by a…
Non-Bloch topological invariants preserve the bulk-boundary correspondence in non-Hermitian topological systems, and are a key concept in the contemporary study of non-Hermitian topology. Here we report the dynamic detection of non-Bloch…
We give a survey on higher invariants in noncommutative geometry and their applications to differential geometry and topology.
Existence of robust edge modes at interfaces of topologically dissimilar systems is one of the most fascinating manifestations of a novel nontrivial state of matter, topological insulators. Such electronic states were originally predicted…
We consider the problem of calculating the weak and strong topological indices in noncentrosymmetric time-reversal (T) invariant insulators. In 2D we use a gauge corresponding to hybrid Wannier functions that are maximally localized in one…
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…
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…
A topological boundary can be formed at the interface between a trivial and a topological insulator. The difference in the topological index across the junction leads to robust gapless surface states. Optical studies of these states are…
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…
In the past decades, topological concepts have emerged to classify matter states beyond the Ginzburg-Landau symmetry breaking paradigm. The underlying global invariants are usually characterized by integers, such as Chern or winding…
The discovery of topological insulators has reformed modern materials science, promising to be a platform for tabletop relativistic physics, electronic transport without scattering, and stable quantum computation. Topological invariants are…
The study of homological invariants such as Tor, Ext and local cohomology modules constitutes an important direction in commutative algebra. Explicit descriptions of these invariants are notoriously difficult to find and often involve…
Two-dimensional (2D) topological electronic insulators are known to give rise to gapless edge modes, which underlie low energy dynamics, including electrical and thermal transport. This has been thoroughly investigated in the context of…
A definition of topological phases of density matrices is presented. The topological invariants in case of both noninteracting and interacting systems are extended to nonzero temperatures. Influence of electron interactions on topological…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
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…
We extend the previously defined many-body marker for two-dimensional $\mathbb{Z}_2$ topological insulators [I. Gilardoni {\it et al.}, Phys. Rev. B {\bf 106}, L161106 (2022)] to distinguish trivial, weak-, and strong-topological insulators…
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…