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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…

Topological band insulators (TBIs) are bulk insulating materials which feature topologically protected metallic states on their boundary. The existing classification departs from time-reversal symmetry, but the role of the crystal lattice…

Topological insulators are a broad class of unconventional materials that are insulating in the interior but conduct along the edges. This edge transport is topologically protected and dissipationless. Until recently, all existing…

Topological band insulators which are dynamically generated by electron-electron interactions have been the- oretically proposed in two and three dimensional lattice models. We present evidence that the two-dimensional version can be…

Two-dimensional (2D) topological insulators (TIs) are promising platforms for low-dissipation spintronic devices based on the quantum spin Hall (QSH) effect, but experimental realization of such systems with a large band gap suitable for…

Topological insulator is a new state of matter which exhibits exotic surface electronic properties. Determining the spin texture of this class of material is of paramount importance for understanding its topological order and can lead to…

Topological phases enable protected transport along the edges of materials, offering immunity against scattering from disorder and imperfections. These phases were suggested and demonstrated not only for electronic systems, but also for…

The quantum spin Hall insulator bismuthene, a two-third monolayer of bismuth on SiC(0001), is distinguished by helical metallic edge states that are protected by a groundbreaking 800 meV topological gap, making it ideal for room temperature…

In this Book Chapter (invited) we briefly review the basic concepts defining topological insulators and focus on elaborating on the key experimental results that revealed and established their symmetry protected (SPT) topological nature. We…

We consider an interface between two strong time-reversal invariant topological insulators having surface states with opposite spin chirality, or equivalently, opposite mirror Chern number. We show that such an interface supports gapless…

The classification of topological insulators predicts the existence of high-dimensional topological phases that cannot occur in real materials, as these are limited to three or fewer spatial dimensions. We use electric circuits to…

We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…

We predict a new family of robust two-dimensional (2D) topological insulators in van der Waals heterostructures comprising graphene and chalcogenides BiTeX (X=Cl, Br and I). The layered structures of both constituent materials produce a…

In a topological insulator, it is the electrons on the surface or edge that carry the signature of topology. Recently, a novel topological state has been proposed in metals or semimetals (gapless) whose band-structure is similar to that of…

In recent years, higher-order topological phases have attracted great interest in various fields of physics. These phases have protected boundary states at lower-dimensional boundaries than the conventional first-order topological phases…

The study of higher-order and real topological states as well as the material realization have become a research forefront of topological condensed matter physics in recent years. Twisted bilayer graphene (tbG) is proved to have…

In rhombohedral-stacked few-layer graphene, the very flat energy bands near the charge neutrality point are unstable to electronic interactions, giving rise to states with spontaneous broken symmetries. Using transport measurements on…

Two-dimensional topological superconductivity has attracted great interest due to the emergence of Majorana modes bound to vortices and propagating along edges. However, due to its rare appearance in natural compounds, experimental…

The study of topological band insulators has revealed fascinating phases characterized by band topology indices and anomalous boundary modes protected by global symmetries. In strongly correlated systems, where the traditional notion of…

Photonic topological states have revolutionized our understanding on the propagation and scattering of light. Recent discovery of higher-order photonic topological insulators opens an emergent horizon for zero-dimensional topological corner…