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Symmetry-protected topological crystalline insulators (TCIs) have primarily been characterized by their gapless boundary states. However, in time-reversal- ($\mathcal{T}$-) invariant (helical) 3D TCI$\unicode{x2014}$termed higher-order TCIs…
In an ideal 3D topological insulator (TI), the bulk is insulating and the surface conducting due to the existence of metallic states that are localized on the surface; these are the topological surface states. Quaternary Bi-based compounds…
The search for inversion asymmetric topological insulators (IATIs) persists as an effect for realizing new topological phenomena. However, so for only a few IATIs have been discovered and there is no IATI exhibiting a large band gap…
Topological insulators (TI), with characteristic Dirac-fermion topological surface states (TSS), have emerged as a new class of electronic materials with rich potentials for both novel physics and device applications. However, a major…
The newly discovered topological crystalline insulators (TCIs) harbor a complex band structure involving multiple Dirac cones. These materials are potentially highly tunable by external electric field, temperature or strain and could find…
Employing ab initio electronic calculations, we propose a new type of two-dimensional (2D) topological insulator (TI), monolayer (ML) low buckled (LB) mercury telluride (HgTe) and mercury selenide (HgSe), with tunable band gaps. Monolayer…
The rich variety of crystalline symmetries in solids leads to a plethora of topological crystalline insulators (TCIs) featuring distinct physical properties, which are conventionally understood in terms of bulk invariants specialized to the…
In typical topological insulator (TI) systems the TI is bordered by a non-TI insulator, and the surrounding conventional insulators, including vacuum, are not generally treated as part of the TI system. Here, we implement the first material…
Topological Kondo insulators (TKIs) are topologically protected insulating states induced not by single-particle band inversions, but by the Kondo interaction between itinerant electrons and a lattice of local magnetic moments. Although…
The topological aspects of electrons in solids emerge in realistic matters as represented by topological insulators. They are expected to show a variety of new magneto-electric phenomena, and especially the ones hosting superconductivity…
Topological insulators (TIs) are a novel class of materials with nontrivial surface or edge states. Time-reversal symmetry (TRS) protected TIs are characterized by the Z2 topological invariant and their helical property becomes lost in an…
Topological Surface States (TSS) represent new types of two dimensional electron systems with novel and unprecedented properties distinct from any quantum Hall-like or spin-Hall effects. Their Z$_2$ topological order can be realized at room…
A three-dimensional (3D) topological insulator (TI) is a quantum state of matter with a gapped insulating bulk yet a conducting surface hosting topologically-protected gapless surface states. One of the most distinct electronic transport…
Topological insulators are materials with an insulating bulk interior while maintaining gapless boundary states against back scattering. Bi$_2$Se$_3$ is a prototypical topological insulator with a Dirac-cone surface state around $\Gamma$.…
Topological insulators (TIs) have attracted much attention due to their spin-polarized surface and edge states, whose origin in symmetry gives them intriguing quantum-mechanical properties. Robust control over the chemical potential of TI…
Lattice defects such as stacking faults may obscure electronic topological features of real materials. In fact, defects are a source of disorder that can enhance the density of states and conductivity of the bulk of the system and they…
We demonstrate, both theoretically and experimentally, the concept of non-linear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of…
The dynamics of two-dimensional (2D) topological quadrupole insulator (TQI) and Chern insulator (CI) after the real-space configuration is transformed from a cylinder or Mobius strip to open boundary condition (OBC) and vice versa is…
Topologically protected gapless edge/surface 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…
The first experimental evidence is presented of the topological insulator state in PbBi$_{2}$Te$_{4}$. A single surface Dirac cone is observed by angle-resolved photoemission spectroscopy (ARPES) with synchrotron radiation. Topological…