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The recent discoveries of higher-order topological insulators (HOTIs) have shifted the paradigm of topological materials, which was previously limited to topological states at boundaries of materials, to those at boundaries of boundaries,…
The modern theory of electric polarization in crystals associates the dipole moment of an insulator with a Berry phase of its electronic ground state [1, 2]. This concept constituted a breakthrough that not only solved the long-standing…
Higher-order topological insulators (HOTIs) are described by symmetric exponentially decayed Wannier functions at some $necessary$ unoccupied Wyckoff positions and classified as obstructed atomic insulators (OAIs) in the topological quantum…
Quadrupole topological insulators are a new class of topological insulators with quantized quadrupole moments, which support protected gapless corner states. The experimental demonstrations of quadrupole-topological insulators were reported…
Higher-order topological insulators (HOTIs) which go beyond the description of conventional bulk-boundary correspondence, broaden the understanding of topological insulating phases. Being mainly focused on electronic materials, HOTIs have…
We report the discovery of several classes of novel topological insulators (TIs) with hybrid-order boundary states generated from the first-order TIs with additional crystalline symmetries. Unlike the current studies on hybrid-order TIs…
Topological states nurtures the emergence of devices with unprecedented functions in photonics, plasmonics, acoustics and phononics. As one of the recently discovered members, higher-order topological insulators (HOTIs) have been…
Topological multipole insulators are a class of higher order topological insulators (HOTI) in which robust fractional corner charges appear due to a quantized electric multipole moment of the bulk. This bulk-corner correspondence has been…
Recent advancements in quantum polarization theory have propelled the exploration of topological insulators (TIs) into the realm of higher-order systems, leading to the study of the celebrated two-dimensional (2D) quadrupole and…
We propose that three-dimensional layered octagonal quasicrystals can host magnetic-field-tunable M\"{o}bius insulators and various higher-order topological insulators (HOTIs), enabled by the interplay of quasicrystalline symmetry and…
Topologically protected gapless edge/surface states are phases of quantum matter which behave as massless Dirac fermions, immunizing against disorders and continuous perturbations. Recently, a new class of topological insulators (TIs) with…
Modern theory of electric polarization is formulated by the Berry phase, which, when quantized, leads to topological phases of matter. Such a formulation has recently been extended to higher electric multipole moments, through the discovery…
In the past years classical wave-systems have constituted an excellent platform for emulating complex quantum phenomena. This approach has been especially fruitful in demonstrating topological phenomena in photonics and acoustics: from…
The discovery and realization of topological insulators, a phase of matter which hosts metallic boundary states when the $d$-dimension insulating bulk is confined to ($d-1$)-dimensions, led to several potential applications. Recently, it…
Topological phases of matter have been extensively studied for their intriguing bulk and edge properties. Recently, higher-order topological insulators with boundary states that are two or more dimensions lower than the bulk states, have…
I consider higher-order topological insulator (HOTI) created in chi(2) nonlinear medium and based on two-dimensional generalization of the Su-Schrieffer-Heeger waveguide array, where transition between trivial and topological phases is…
Recently, a new class of second-order topological insulators (SOTIs) characterized by an electronic dipole has been theoretically introduced and proposed to host topological corner states. As a novel topological state, it has been…
Two new recently proposed classes of topological phases, namely fractons and higher order topological insulators (HOTIs), share at least superficial similarities. The wide variety of proposals for these phases calls for a universal field…
Quadrupole topological insulator, which supports robust corner states, has been recently demonstrated in two-dimensional (2D) spatial lattices. Here, we design the first photonic quadrupole topological insulator in fully synthetic spaces…
Exploring novel topological matters with exotic quantum states has always been a core issue in the field of condensed matter physics, which can update the understanding of topological phases and broaden the classification of topological…