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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…
In this work we consider whether nonsymmorphic symmetries such as a glide plane can protect the existence of topological crystalline insulators and superconductors in three dimensions. In analogy to time-reversal symmetric insulators, we…
We explore the bulk-edge correspondence for topological insulators (superconductors) without time-reversal symmetry from the point of view of the index theorem for open spaces. We assume generic Hamiltonians not only with a linear…
Topological corner states are exotic topological boundary states that are bounded to zero-dimensional geometry even the dimension of systems is large than one. As an elegant physical correspondence, their numbers are dictated by the bulk…
Higher-order topological insulator (HOTI) represents a new phase of matter, the characterization of which goes beyond the conventional bulk-boundary correspondence and is attracting significant attention by the broad community. Using a…
In two dimensions, magnetic higher-order topological insulators (HOTIs) are characterized by excess boundary charge and a compensating bulk ``filling anomaly.'' At the same time, without additional noncrystalline symmetries, the boundaries…
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…
We establish an analytic low-energy theory describing higher-order topological insulator (HOTI) phases in quasicrystalline systems. We apply this to a model consisting of two stacked Haldane models with oppositely propagating edge modes,…
We provide an index-theoretic proof of the bulk-boundary correspondence for two- and three-dimensional second-order topological insulators that preserve inversion symmetry, which are modeled as rectangles and rectangular prism-shaped…
In two-dimensional systems with space-time inversion symmetry, such as $C_{2z}T$, the reality condition on wave functions gives rise to real band topology characterized by the Euler class, a $\mathbb{Z}$-valued topological invariant for a…
The studies of topological phases of matter have been extended from condensed matter physics to photonic systems, resulting in fascinating designs of robust photonic devices. Recently, higher-order topological insulators (HOTIs) have been…
Establishing the fundamental relation between the homotopy invariants and the band topology of Hamiltonians has played a critical role in the recent development of topological phase research. In this work, we establish the homotopy…
We propose second-order topological insulators (SOTIs) whose lattice structure has the hexagonal symmetry $C_{6}$ in three and two dimensions. We start with a three-dimensional weak topological insulator constructed on the stacked…
We construct microscopical models of one-dimensional non-interacting topological insulators in all of the chiral universality classes. Specifically, we start with a deformation of the Su-Schrieffer-Heeger (SSH) model that breaks…
The prediction of non-trivial topological phases in Bloch insulators in three dimensions has recently been experimentally verified. Here, I provide a picture for obtaining the $Z_{2}$ invariants for a three dimensional topological insulator…
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…
We define a $\mathbb{Z}_2$-valued topological and gauge invariant associated to any 1-dimensional, translation-invariant topological insulator which satisfies either particle-hole symmetry or chiral symmetry. The invariant can be computed…
The discovery of higher-order topological insulator (HOTI) has established a new paradigm for understanding symmetry-constrained boundary electronic states. Here, based on first-principles calculations, we demonstrate the emergence of HOTI…
Quantum spin Hall insulators, or synonymously known as 2D topological insulators, are crucial 2D systems hosting topologically protected edge states. The working temperature of this topological quantum phase is dictated by the inverted…
The higher order topological insulator (HOTI) has enticed enormous research interests owing to its novelty in supporting gapless states along the hinges of the crystal. Despite several theoretical predictions, enough experimental…