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Topological phononics extends the foundational concepts of topological condensed matter physics to the realm of lattice vibrations and classical mechanical waves, unlocking robust, defect-immune states and phenomena beyond the reach of…
Floquet higher order topological insulators (FHOTIs) are a novel topological phase that can occur in periodically driven lattices. An appropriate experimental platform to realize FHOTIs has not yet been identified. We introduce a…
We study the quantized charge pumping of higher-order topological insulators (HOTIs) with edge-corner correspondences based on the combination of the rotation of in-plane magnetic field and the quantum spin Hall effect. A picture of a…
Topologically protected gapless edge 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…
A powerful result of topological band theory is that nontrivial phases manifest obstructions to constructing localized Wannier functions. In Chern insulators, it is impossible to construct Wannier functions that respect translational…
We study positions of chiral hinge states in higher-order topological insulators (HOTIs) with inversion symmetry. First, we exhaust all possible configurations of the hinge states in the HOTIs in all type-I magnetic space groups with…
Second-order topological insulator (SOTI) is featured with the presence of $(d-2)$-dimensional boundary states in $d$-dimension systems. The non-Hermiticity induced breakdown of bulk-boundary correspondence (BBC) and the periodic driving on…
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…
The modern theory of charge polarization in solids is based on a generalization of Berry's phase. Its possible quantization lies at the heart of our understanding of all systems with topological band structures that were discovered over the…
We argue that various kinds of topological insulators (TIs) can be insightfully characterized by an inspection of the charge centers of the hybrid Wannier functions, defined as the orbitals obtained by carrying out a Wannier transform on…
We present a theoretical study and experimental realization of a system that is simultaneously a four-dimensional (4D) Chern insulator and a higher-order topological insulator (HOTI). The system sustains the coexistence of (4-1)-dimensional…
In recent years, there has been a surge of interest in higher-order topological phases (HOTPs) across various disciplines within the field of physics. These unique phases are characterized by their ability to harbor topological protected…
We propose two mechanisms to realize the second order topological insulator (SOTI) state in spinless hexagonal lattices, viz., chemical modification and anti-Kekul\'e/Kekul\'e distortion of hexagonal lattice. Correspondingly, we construct…
Second-order photonic topological insulators that host highly localized corner states resilient to defects, are opening new routes towards developing fascinating photonic devices. However, the existing works on second-order photonic…
Higher-order topological insulators harbor unique corner modes that hold immense potential for applications in information storage. However, the practical manipulation of these states has been constrained by the fixed positions and energies…
In $strong$ topological insulators protected surface states are always manifest, while in $weak$ topological insulators (WTI) the corresponding metallic surface states are either manifest or hidden, depending on the orientation of the…
The modern understanding of topological insulators is based on Wannier obstructions in position space. Motivated by this insight, we study topological superconductors from a position-space perspective. For a one-dimensional superconductor,…
Higher-order topological (HOT) phases feature boundary (such as corner and hinge) modes of codimension $d_c>1$. We here identify an \emph{antiunitary} operator that ensures the spectral symmetry of a two-dimensional HOT insulator and the…
Topological insulators (TIs) are materials that have a bulk electronic band gap like an ordinary insulator but have protected conducting states on their surface. One of the most interesting properties of TIs is their spin helicity, whereby…
Notion of square-root topological insulators have been recently generalized to higher-order topological insulators. In two-dimensional square-root higher-order topological insulators, emergence of in-gap corner states are inherited from the…