Related papers: Corner states are not topologically protected

Bulk-boundary correspondence serves as an important feature of the strong topological insulators, including Chern insulators and $Z_2$ topological insulators. Under nontrivial band topology, the protected gapless edge states correspond to…

Topological invariants are conventionally known to be responsible for protection of extended states against disorder. A prominent example is the presence of topologically protected extended-states in two-dimensional (2D) quantum Hall…

Topological materials are often characterized by unique edge states which are in turn used to detect different topological phases in experiments. Recently, with the discovery of various higher-order topological insulators, such spectral…

We prove the existence of higher-order topological insulators in: {\it i}) fourfold rotoinversion invariant bulk crystals, and {\it ii}) inversion-symmetric systems with or without an additional three-fold rotation symmetry. These states of…

In the presence of crystalline symmetries, second-order topological insulators can be featured by the polarization which is believed identical to the Wannier center. In this Letter, we show that second-order topological insulators are…

Second-order topological insulators can be characterized by their bulk polarization, which is believed to be intrinsically connected to the center of the Wannier function. In this study, we demonstrate the existence of second-order…

Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…

We demonstrate that the presence of a localized state at the corner of an insulating domain is not always a predictor of a certain non-trivial higher-order topological invariant, even though they appear to co-exist in the same Hamiltonian…

We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of…

While topological phases have been extensively studied in amorphous systems in recent years, it remains unclear whether the random nature of amorphous materials can give rise to higher-order topological phases that have no crystalline…

The bulk-boundary correspondence is a generic feature of topological states of matter, reflecting the intrinsic relation between topological bulk and boundary states. For example, robust edge states propagate along the edges and corner…

Recently there is trend to study topological properties in one-dimensional(1D) periodic systems. Concepts such as Zak phase are considered as topological invariants that characterize the bulk bands. The bulk 1D systems are classified to…

It is often thought that emergent phenomena in topological phases of matter are destroyed when tuning to a critical point. In particular, topologically protected edge states supposedly delocalize when the bulk correlation length diverges.…

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…

In commonly employed models for 2D topological insulators, bulk gapless states are well known to form at the band inversion points where the degeneracy of the states is protected by symmetries. It is thus sometimes quite tempting to…

We provide evidence that, alongside topologically protected edge states, two-dimensional Chern insulators also support localised bulk states deep in their valance and conduction bands. These states manifest when local potential gradients…

We numerically verify and analytically prove a winding number invariant that correctly predicts the number of edge states in one-dimensional, nearest-neighbor (between unit cells), two-band models with any complex couplings and open…

Compared with conventional topological insulator that carries topological state at its boundaries, the higher-order topological insulator exhibits lower-dimensional gapless boundary states at its corners and hinges. Leveraging the form…

I study theoretically quadrupolar topological insulators under applied static electric field rotated along the crystal axis. I demonstrate, that the energy spectrum of this structure is a Wannier-Stark ladder that is quantized and directly…

Two-dimensional second-order topological insulators are characterized by the presence of topologically protected zero-energy bound states localized at the corners of a flake. In this paper we theoretically study the occurrence and features…