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We study surface states of topological crystalline insulators and superconductors protected by inversion symmetry. These fall into the category of "higher-order" topological insulators and superconductors which possess surface states that…
Electrons hopping on the sites of a three-dimensional pyrochlore lattice are shown to form topologically non-trivial insulating phases when the spin-orbit (SO) coupling and lattice distortions are present. Of 16 possible topological classes…
We investigate the bulk-boundary correspondence in two-dimensional type-I semi-Dirac materials with band inversion and Rashba spin-orbit coupling. Employing a dimensional reduction framework, we identify the Zak phase along the…
Presence of entangled states is explicitly shown in Topological insulator (TI) $Bi_2Te_3$. The surface and bulk state are found to have the different structures of entanglement. The surface states live as maximally entangled states in the…
Engineered lattices in condensed matter physics, such as cold atom optical lattices or photonic crystals, can have fundamentally different properties from naturally-occurring electronic crystals. Here, we report a novel type of artificial…
Topological insulators as new type of quantum matter materials are characterized by a full insulating gap in the bulk and gapless edge/surface states which are protected by time-reversal symmetry. We propose the interference patterns caused…
Twisting the stacking of layered materials leads to rich new physics. A three dimensional (3D) topological insulator film host two dimensional gapless Dirac electrons on top and bottom surfaces, which, when the film is below some critical…
The electronic band structure of iron pnictides exhibits four Dirac cones, which are due to crystal symmetry and orbital bonding orientation. This hallmark signature presents the pnictide family as an ideal candidate in the search for…
Although multilayer systems possess global inversion symmetry, some of the layers lack local inversion symmetry because no global inversion centers are present on such layers. Such locally non-centrosymmetric systems exhibit spatially…
Although many possible two-dimensional (2D) topological insulators (TIs) have been predicted in recent years, there is still lack of experimentally realizable 2D TI. Through first-principles and tight-binding simulations, we found an…
Topologically protected edge channels show prospects for quantum devices. They have been found experimentally in two-dimensional (2D) quantum spin Hall insulators (QSHIs), weak topological insulators and higher-order topological insulators…
Recently discovered photonic higher-order topological insulators enable unprecedented flexibility in the robust localization of light in structures of different dimensionality. While the potential of the two-dimensional systems is currently…
Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional…
We explore a new way of producing the Rashba spin-orbit coupling (SOC) for ultracold atoms by using a two-component (spinor) atomic Bose-Einstein condensate (BEC) confined in a bilayer geometry. The SOC of the Rashba type is created if the…
Crystalline topological insulators have recently become a powerful platform for realizing photonic topological states from microwaves to the visible. Appropriate geometric symmetries of the lattice are at the core of their functionality.…
Second-order topological insulators and superconductors have a gapped excitation spectrum in bulk and along boundaries, but protected zero modes at corners of a two-dimensional crystal or protected gapless modes at hinges of a…
Higher-order topological insulator, as a newly found non-trivial material and structure, possesses a topological phase beyond the bulk-boundary correspondence. Here, we present an experimental observation of photonic higher-order…
Phase-change materials are ubiquitous in technology because of their ability to transition between amorphous and crystalline phases fast and reversibly, upon shining light or passing a current. Here we argue that to fully understand their…
Higher Order Topological Insulators (HOTI) are $d$-spatial dimensional systems featuring topologically protected gap-less states at their $(d-n)$-dimensional boundaries. With the help of \textit{ab-initio} calculations and tight binding…
We report the discovery of weak topological insulators by ab initio calculations in a honeycomb lattice. We propose a structure with an odd number of layers in the primitive unit-cell as a prerequisite for forming weak topological…