Related papers: Bulk-boundary correspondence in three dimensional …
We analyze the topological $\mathbb{Z}_2$ invariant, which characterizes time reversal invariant topological insulators, in the framework of index theory and K-theory. The topological $\mathbb{Z}_2$ invariant counts the parity of…
Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in $3$D with $C_n$ lattice rotation…
Recent developments in the study of topological defects highlight the importance of understanding the multi-dimensional structure of bulk excitations inside a quantum system. When the bulk ground state is trivial, i.e. a product state,…
We study the correspondence between boundary spectrum of non-chiral topological orders on an open manifold $\mathcal{M}$ with gapped boundaries and the entanglement spectrum in the bulk of gapped topological orders on a closed manifold. The…
For a wide class of noninteracting tight-binding models in one dimension we present an analytical solution for all scattering and edge states on a half-infinite system. Without assuming any symmetry constraints we consider models with…
Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often deviates the edge anticrossing even into the bulk, where corner…
Bulk-boundary correspondence is the cornerstone of topological physics. In some non-Hermitian topological system this fundamental relation is broken in the sense that the topological number calculated for the Bloch energy band under the…
Topological insulators as new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states which are protected by time-reversal symmetry. We propose the interference patterns caused…
Topological phases stabilized by crystalline point group symmetry protection are a large class of symmetry-protected topological phases subjected to considerable experimental scrutiny. Here, we show that the canonical three-dimensional (3D)…
As first demonstrated by the characterization of the quantum Hall effect by the Chern number, topology provides a guiding principle to realize robust properties of condensed matter systems immune to the existence of disorder. The…
Bulk-edge correspondence, with quantized bulk topology leading to protected edge states, is a hallmark of topological states of matter and has been experimentally observed in electronic, atomic, photonic, and many other systems. While…
The boundary of a topological insulator (TI) hosts an anomaly restricting its possible phases: e.g. 3D strong and weak TIs maintain surface conductivity at any disorder if symmetry is preserved on-average, at least when electron…
In topological phases of matter for which the bulk and boundary support distinct electronic gaps, there exists the possibility of decoupled mobility gaps in the presence of disorder. This is in analogy with the well-studied problem of…
We show that the bulk-boundary correspondence for topological insulators can be modified in the presence of non-Hermiticity. We consider a one-dimensional tight-binding model with gain and loss as well as long-range hopping. The system is…
Higher-order topological insulators have a modified bulk-boundary correspondence compared to other topological phases: instead of gapless edge or surface states, they have gapped edges and surfaces, but protected modes at corners or hinges.…
We investigated the electronic properties of the topological insulator Bi$_{2}$Te$_{3}$ by scanning tunneling microscopy and spectroscopy at low temperature. We obtained high-resolution quasiparticle interference data of the topological…
We describe a three-dimensional crystalline topological insulator (TI) phase of matter that exhibits spontaneous polarization. This polarization results from the presence of (approximately) flat bands on the surface of such TIs. These flat…
It has been recently realized that strong interactions in topological Bloch bands give rise to the appearance of novel states of matter. Here we study connections between these systems -- fractional Chern insulators and the fractional…
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…
Spin-orbit coupled materials have attracted revived prominent research interest as of late, especially due their direct connection with topological notions. Arguably, a hallmark of this pursuit is formed by the concept of the topological…