Related papers: Nonlinear quadrupole topological insulators
Extensive recent research on Lieb and kagome lattices highlights their unique physics characterized by the coexistence of Dirac points, van Hove singularities, and flat bands. In these models, flat bands are typically pinned at the center…
Higher-order topological phases (HOTPs) feature protected gapless modes on boundaries of higher codimension, such as the corners or hinges of a crystal. They are understood as being protected by lattice symmetries: If the latter are broken,…
Higher-order topological insulators, which support lower-dimensional topological boundary states than the first-order topological insulators, have been intensely investigated in the integer dimensional systems. Here, we provide a new…
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…
Recent acoustic and electrical-circuit experiments have reported the third-order (or octupole) topological insulating phase, while its counterpart in classical magnetic systems is yet to be realized. Here we explore the collective dynamics…
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 generalize the Pfaffian formalism, which has been playing an important role in the study of time-reversal invariant topological insulators (TIs), to 3D chiral higher-order topological insulators (HOTIs) protected by the product of…
Pursuing topological phase and matter in a variety of systems is one central issue in current physical sciences and engineering. Motivated by the recent experimental observation of corner states in acoustic and photonic structures, we…
Bosonic topological insulators (BTI) in three dimensions are symmetry-protected topological phases (SPT) protected by time-reversal and boson number conservation {symmetries}. BTI in three dimensions were first proposed and classified by…
Higher-order topological phases (HOTPs) are characterized by symmetry-protected bound states at the corners or hinges of the system. In this work, we reveal a momentum-space counterpart of HOTPs in time-periodic driven systems, which are…
Nanostructures, such a quantum dots or nanoparticles, made of three-dimensional topological insulators (3DTIs) have been recently attracting increasing interest, especially for their optical properties. In this paper we calculate the energy…
The higher-order topological insulators (HOTIs), with such as the topological corner states, emerge as a thriving topic in the field of topological physics. But few connections have been found for the HOTIs with the well explored…
The defining feature of topological insulators is that their valence states are not continuously deformable to a suitably defined atomic limit without breaking the symmetry or closing the energy gap. When the atomic limit is given by…
We propose a cold-atom setup which allows for a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. We further show…
Higher-order topological insulators have been introduced in the precursory Benalcazar-Bernevig-Hughes quadrupole model, but no electronic compound has been proposed to be a quadrupole topological insulator (QTI) yet. In this work, we…
We study the higher-order topological insulators at finite temperature based on a generalized real-space quadrupole moment, which extends the ground state expectations to ensemble averages. Our study reveals that chiral symmetry alone…
Higher-order topological band theory has transformed the landscape of topological phases in quantum and classical systems. Here, we experimentally demonstrate a two-dimensional (2D) higher-order topological phase (HOTP), referred to as the…
Recent theoretical studies have extended the Berry phase framework to account for higher electric multipole moments, quadrupole and octupole topological phases have been proposed. Although the two-dimensional quantized quadrupole insulators…
We introduce a two-dimensional network model that realizes a higher-order topological phase (HOTP). We find that in the HOTP the bulk and boundaries of the system are gapped, and a total of 16 corner states are protected by the combination…
Three dimensional (3D) third-order topological insulators (TIs) have zero-dimensional (0D) corner states, which are three dimensions lower than bulk. Here we investigate the third-order TIs on breathing pyrochlore lattices with p-orbital…