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19세기말 애국적 담론과 新小說의 정체성

Higher-order topological insulators1–5 are a family of recently predicted topological phases of matter that obey an extended topological bulk–boundary correspondence principle. For example, a two-dimensional (2D) second-order topological insulator does not exhibit gapless one-dimensional (1D) topological edge states, like a standard 2D topological insulator, but instead has topologically protected zero-dimensional (0D) corner states. The first prediction of a second-order topological insulator1, based on quantized quadrupole polarization, was demonstrated in classical mechanical6 and electromagnetic7,8 metamaterials. Here we experimentally realize a second-order topological insulator in an acoustic metamaterial, based on a ‘breathing’ kagome lattice9 that has zero quadrupole polarization but a non-trivial bulk topology characterized by quantized Wannier centres2,9,10. Unlike previous higher-order topological insulator realizations, the corner states depend not only on the bulk topology but also on the corner shape; we show experimentally that they exist at acute-angled corners of the kagome lattice, but not at obtuse-angled corners. This shape dependence allows corner states to act as topologically protected but reconfigurable local resonances. A second-order topological insulator in an acoustical metamaterial with a breathing kagome lattice, supporting one-dimensional edge states and zero-dimensional corner states is demonstrated.

/pdf/acoustic-higher-order-topological-insulator-on-a-kagome-2szcjantih.pdf

Acoustic higher-order topological insulator on a kagome lattice.

Topological systems are inherently robust to disorder and continuous perturbations, resulting in dissipation-free edge transport of electrons in quantum solids, or reflectionless guiding of photons and phonons in classical wave systems characterized by topological invariants. Recently, a new class of topological materials characterized by bulk polarization has been introduced, and was shown to host higher-order topological corner states. Here, we demonstrate theoretically and experimentally that 3D-printed two-dimensional acoustic meta-structures can possess nontrivial bulk topological polarization and host one-dimensional edge and Wannier-type second-order zero-dimensional corner states with unique acoustic properties. We observe second-order topological states protected by a generalized chiral symmetry of the meta-structure, which are localized at the corners and are pinned to 'zero energy'. Interestingly, unlike the 'zero energy' states protected by conventional chiral symmetry, the generalized chiral symmetry of our three-atom sublattice enables their spectral overlap with the continuum of bulk states without leakage. Our findings offer possibilities for advanced control of the propagation and manipulation of sound, including within the radiative continuum.

Observation of higher-order topological acoustic states protected by generalized chiral symmetry.

Here, higher-order topological insulators and superconductors protected by inversion symmetry are investigated. These phases are characterized by gapped bulk and surface with gapless modes confined to hinges or corners of the sample. Such surface states can be understood as topological defects that are globally stabilized by inversion. They can be built using a layer construction that embeds a standard topological insulator/superconductor into a higher dimension by symmetrically adding to it copies of itself. Using this procedure, a complete classification of such states in any dimension is obtained and several examples for possible physical realizations are provided.

Higher-order topological insulators and superconductors protected by inversion symmetry

While topological insulators have a gapped bulk band structure, they have gapless surface states. Recently, it was shown that the presence of additional crystalline symmetries can lead to topological phases that combine a gapped bulk spectrum with gapless states on edges or corners of the crystal. Such topological phases have been called ``higher-order topological phases''. This article presents a complete classification of second-order topological insulators and superconductors with mirror, twofold-rotation, or inversion symmetry. The authors show that crystals with a mirror symmetry and a nontrivial bulk band structure either have gapless surfaces or gapless edges. On the other hand, there are crystals with twofold rotation or inversion symmetry with a nontrivial bulk topology but without surface or edge states.

/pdf/second-order-topological-insulators-and-superconductors-with-dxydzga7py.pdf

Second-order topological insulators and superconductors with an order-two crystalline symmetry

Determining the topological phases in crystalline systems requires a complete set of topological invariants, whose definition and evaluation is, in general, a complicated task. Symmetry-based indicators, such as the Fu-Kane formula for inversion-symmetric topological insulators, utilize the crystalline symmetry to define easy-to-compute topological invariants. These indicators can be generalized to extract the maximal information about the topology of the band structure and of the associated anomalous boundary states from data at the high-symmetry momenta only. Using the concept of relative topology, the authors show how to construct symmetry-based indicators for band superconductors.

/pdf/symmetry-based-indicators-for-topological-bogoliubov-de-18r05t8i3g.pdf

Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians

We discuss a pairing mechanism in interacting two-dimensional multipartite lattices that intrinsically leads to a second order topological superconducting state with a spatially modulated gap. When the chemical potential is close to Dirac points, oppositely moving electrons on the Fermi surface undergo an interference phenomenon in which the Berry phase converts a repulsive electron-electron interaction into an effective attraction. The topology of the superconducting phase manifests as gapped edge modes in the quasiparticle spectrum and Majorana Kramers pairs at the corners. We present symmetry arguments which constrain the possible form of the electron-electron interactions in these systems and classify the possible superconducting phases which result. Exact diagonalization of the Bogoliubov-de Gennes Hamiltonian confirms the existence of gapped edge states and Majorana corner states, which strongly depend on the spatial structure of the gap. Possible applications to vanadium-based superconducting kagome metals AV$_3$Sb$_3$ (A=K,Rb,Cs) are discussed.

Higher-order topological superconductivity from repulsive interactions in kagome and honeycomb systems

We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations -- topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct $d$-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to $(d-2)$-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

/pdf/bulk-boundary-defect-correspondence-at-disclinations-in-3ehkewdfs1.pdf

Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors.

We study a link between the ground-state topology and the topology of the lattice via the presence of anomalous states at disclinations – topological lattice defects that violate a rotation symmetry only locally. We first show the existence of anomalous disclination states, such as Majorana zero-modes or helical electronic states, in second-order topological phases by means of Volterra processes. Using the framework of topological crystals to construct d-dimensional crystalline topological phases with rotation and translation symmetry, we then identify all contributions to (d − 2)-dimensional anomalous disclination states from weak and first-order topological phases. We perform this procedure for all Cartan symmetry classes of topological insulators and superconductors in two and three dimensions and determine whether the correspondence between bulk topology, boundary signatures, and disclination anomaly is unique.

/pdf/bulk-boundary-defect-correspondence-at-disclinations-in-3izbw4i4bm.pdf

Max Geier

Papers

Second-order topological insulators and superconductors with an order-two crystalline symmetry

Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians

Higher-order topological superconductivity from repulsive interactions in kagome and honeycomb systems

Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors.

Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors