Related papers: Topological defect-mediated corner states and high…
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…
Higher-order topological insulators have triggered great interests because of exhibitions of non-trivial bulk topology on lower-dimensional boundaries like corners and hinges. While such interesting phases have been investigated in a…
In insulating crystals, it was previously shown that defects with two fewer dimensions than the bulk can bind topological electronic states. We here further extend the classification of topological defect states by demonstrating that the…
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…
A $d$-dimensional second-order topological insulator (SOTI) can host topologically protected $(d - 2)$-dimensional gapless boundary modes. Here we show that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to…
Topological phases with insulating bulk and gapless surface or edge modes have attracted much attention because of their fundamental physics implications and potential applications in dissipationless electronics and spintronics. In this…
The zero-mode corner states in the gap of two-dimensional non-Hermitian Su-Schrieffer-Heeger model are robust to infinitesimal perturbations that preserve chiral symmetry. However, we demonstrate that this general belief is no longer valid…
We complete a classification of topological phases and their topological defects in crystalline insulators and superconductors. We consider topological phases and defects described by non-interacting Bloch and Bogoliubov de Gennes…
Higher-order topological phases of matter have been extensively studied in various areas of physics. While the Aubry-Andr\'e-Harper model provides a paradigmatic example to study topological phases, it has not been explored whether a…
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…
Topologically gapless edge states, characterized by topological invariants and Berry's phases of bulk energy bands, provide amazing techniques to robustly control the reflectionless propagation of electrons, photons and phonons. Recently, a…
Recently, higher-order topological phases that do not obey the usual bulk-edge correspondence principle have been introduced in electronic insulators and brought into classical systems, featuring with in-gap corner/hinge states. So far,…
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…
Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional…
A two-dimensional second-order topological insulator exhibits topologically protected zero-energy states at its corners. In the literature, the breathing kagome lattice with nearest-neighbor hopping is often mentioned as an example of a…
Higher-order topological insulators are established as topological crystalline insulators protected by crystalline symmetries. One celebrated example is the second-order topological insulator in three dimensions that hosts chiral hinge…
We propose a realization of a two-dimensional higher-order topological insulator with ultracold atoms loaded into orbital angular momentum (OAM) states of an optical lattice. The symmetries of the OAM states induce relative phases in the…
We theoretically investigate the engineering of two-dimensional second-order topological insulators with corner states by coupling two first-order topological insulators. We find that the interlayer coupling between two topological…
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…
Recently there is a surge of interests in the so-called topologically protected corner states in 2D and 3D systems. Such systems are considered as high order topological insulators. Wannier centers are used as topological invariants to…