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The recently discovered three dimensional or bulk topological insulators are expected to exhibit exotic quantum phenomena. It is believed that a trivial insulator can be twisted into a topological state by modulating the spin-orbit…
The bulk-boundary correspondence of the second-order topological insulator (SOTI) has been well established, but a universal transport signature for open systems is still absent. For a variety of SOTIs induced by applying in-plane magnetic…
Topological Kondo insulators (TKIs) are new type of symmetry-protected topological insulators, which develop through the interplay of strong correlations and spin-orbit interactions. In these materials, the bulk is a perfect band insulator…
Many efforts have been made in the past decade to realize topological superconductivity using superconducting proximity effect, but an ideal platform is still lacking. A 3D topological insulator (TI) is promising for this purpose due to the…
We analyze the topological $\mathbb{Z}_2$ invariant, which characterizes time reversal invariant topological insulators, in the framework of index theory and K-theory. The topological $\mathbb{Z}_2$ invariant counts the parity of…
Physical phenomena driven by topological properties, such as the quantum Hall effect, have the appealing feature to be robust with respect to external perturbations. Lately, a new class of materials has emerged manifesting their topological…
We study the topological structure of matter-light excitations, so called polaritons, in a quantum spin Hall insulator coupled to photonic cavity modes. We identify a topological invariant in the presence of time reversal (TR) symmetry, and…
Evidence for the quantum spin Hall (QSH) effect has been reported in several experimental systems in the form of approximately quantized edge conductance. However, the most fundamental feature of the QSH effect, spin-momentum locking in the…
Quantized responses are important tools for understanding and characterizing the universal features of topological phases of matter. In this work, we consider a class of topological crystalline insulators in $3$D with $C_n$ lattice rotation…
Topological insulators (TIs) are renowned for their remarkable electronic properties: quantised bulk Hall and edge conductivities, and robust edge wave-packet propagation, even in the presence of material defects and disorder. Computations…
We study the effect of spin-momentum locking inhomogeneity on the planar Hall effect in topological insulators (TIs). Using the minimal model describing surface states of 3D TIs and semiclassical Boltzmann formalism, we have derived the…
Topological insulators~(TIs) are a new class of materials that resemble ordinary band insulators in terms of a bulk band gap but exhibit protected metallic states on their boundaries. In this modern direction, higher-order TIs~(HOTIs) are a…
Topological invariants are a significant ingredient in the study of topological phases of matter that intertwines the supposedly contradicting concepts of bulk and boundary. The nature of the invariants differ depending on the dimension of…
We study three dimensional generalizations of the quantum spin Hall (QSH) effect. Unlike two dimensions, where the QSH effect is distinguished by a single $Z_2$ topological invariant, in three dimensions there are 4 invariants…
The topological insulator is an electronic phase stabilized by spin-orbit coupling that supports propagating edge states and is not adiabatically connected to the ordinary insulator. In several ways it is a spin-orbit-induced analogue in…
High-order topological insulators (TIs) are a family of recently-predicted topological phases of matter obeying an extended topological bulk-boundary correspondence principle. For example, a two-dimensional (2D) second-order TI does not…
Topological insulators are physically distinguishable from normal insulators only near edges and defects, while in the bulk there is no clear signature to their topological order. In this work we show that the Z index of topological…
Topological insulators are characterized by a nontrivial band topology driven by the spin-orbit coupling. To fully explore the fundamental science and application of topological insulators, material realization is indispensable. Here we…
The past decade's apparent success in predicting and experimentally discovering distinct classes of topological insulators (TIs) and semimetals masks a fundamental shortcoming: out of 200,000 stoichiometric compounds extant in material…
We prove a general theorem on the relation between the bulk topological quantum number and the edge states in two dimensional insulators. It is shown that whenever there is a topological order in bulk, characterized by a non-vanishing Chern…