Related papers: Topological Gyromorphs
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…
Topological insulators have been extended to higher-order versions that possess topological hinge or corner states in lower dimensions. However, their robustness against disorder is still unclear. Here, we theoretically investigate the…
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped phases in 1D systems can be completely characterized using tools related to projective representations of the…
Non-Hermiticity appears ubiquitously in various open classical and quantum systems and enriches classification of topological phases. However, the role of nonsymmorphic symmetry, crystalline symmetry accompanying fractional lattice…
Topological insulators are new states of quantum matter with metallic edge/surface states. In this paper, we pointed out that there exists a new type of particle-hole symmetry-protected topological insulator - topological hierarchy…
We study topological states of matter in quasicrystals, which do not rely on crystalline orders. In the absence of a bandstructure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a…
A topological insulator is regarded as an ideal candidate for information storage and high-speed lossless electrical transmission devices due to robust topological protected boundary modes. Previous studies revealed that symmetry exerts an…
Photonic topological insulators (PTIs) exhibit robust photonic edge states protected by band topology, similar to electronic edge states in topological band insulators. Standard band theory does not apply to amorphous phases of matter,…
Topological crystalline insulators (TCI) possess electronic states protected by crystal symmetries, rather than time-reversal symmetry. We show that the transition metal oxides with heavy transition metals are able to support nontrivial…
We study non-interacting electrons in disordered one-dimensional materials which exhibit a spectral gap, in each of the ten Altland-Zirnbauer symmetry classes. We define an appropriate topology on the space of Hamiltonians so that the…
Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on…
We show that the chiral Dirac and Majorana hinge modes in three-dimensional higher-order topological insulators (HOTIs) and superconductors (HOTSCs) can be gapped while preserving the protecting $\mathsf{C}_{2n}\mathcal T$ symmetry upon the…
We introduce novel higher-order topological phases of matter in chiral-symmetric systems (class AIII of the tenfold classification), most of which would be misidentified as trivial by current theories. These phases are protected by…
We describe recent progress in our understanding of the interplay between interactions, symmetry, and topology in states of quantum matter. We focus on a minimal generalization of the celebrated topological band insulators to interacting…
In this work, we study the generalization of decohered average symmetry-protected topological phases to open quantum systems with a combination of subsystem symmetries and global symmetries. In particular, we provide examples of two types…
We classify insulators by generalized symmetries that combine space-time transformations with quasimomentum translations. Our group-cohomological classification generalizes the nonsymmorphic space groups, which extend point groups by…
We discuss systems which have some, but not all of the hallmarks of topological phases. These systems' topological character is not fully captured by a local order parameter, but they are also not fully described at low energies by…
Topological phases of matter are ubiquitous in crystals, but less is known about their existence in amorphous systems, that lack long-range order. In this perspective, we review the recent progress made on theoretically defining amorphous…
The emerging field of topology has brought device effects to a new level. Higher-order topological insulators (HOTIs) go beyond traditional descriptions of bulk-edge correspondence, broadening the understanding of topologically insulating…
We consider topological phases in periodically driven (Floquet) systems exhibiting many-body localization, protected by a symmetry $G$. We argue for a general correspondence between such phases and topological phases of undriven systems…