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Photonic crystal topological insulators host protected states at their edges. In the band structure these edge states appear as continuous bands crossing the photonic band gap. They allow light to propagate unidirectionally and without…
Moir\'e materials have become one of the most active fields in material science in recent years due to their high tunability, and their unique properties emerge from the Moir\'e-scale structure modulation. Here, we propose twisted bilayer…
Discovery of novel topological orders of condensed matters is of a significant interest in both fundamental and applied physics due to the associated quantum conductance behaviors and unique symmetry-protected backscattering-immune…
Gapless bilayer graphene is susceptible to a variety of spontaneously gapped states. As predicted by theory and observed by experiment, the ground state is however topologically trivial, because a valley-independent gap is energetically…
The rapid development of topological photonics and acoustics calls for accurate understanding of band topology in classical waves, which is not yet achieved in many situations. Here, we present the Wilson-loop approach for exact numerical…
Quadrupole topological insulators are a new class of topological insulators with quantized quadrupole moments, which support protected gapless corner states. The experimental demonstrations of quadrupole-topological insulators were reported…
For the classification of topological phases of matter, an important consideration is whether a system is spinless or spinful, as these two classes have distinct symmetry algebra that gives rise to fundamentally different topological…
Higher-order topological insulators are newly proposed topological phases of matter, whose bulk topology manifests as localized modes at two- or higher-dimensional lower boundaries. In this work, we propose the twisted bilayer graphenes…
Time-variant systems have recently garnered considerable attention due to their unique potentials in manipulating electromagnetic waves. Here, a novel class of topological spacetime crystals is introduced, with a traveling-wave modulation…
Topological insulators are materials that conduct on the surface and insulate in their interior due to non-trivial topological order. The edge states on the interface between topological (non-trivial) and conventional (trivial) insulators…
Valley pseudospin, a new degree of freedom in photonic lattices, provides an intriguing way to manipulate photons and enhance the robustness of optical networks. Here we experimentally demonstrated topological waveguiding, refracting,…
Recently, higher-order topological insulators have been attracting extensive interest. Unlike the conventional topological insulators that demand bulk gap closings at transition points, the higher-order band topology can be changed without…
It was recently shown that a chiral topological phase emerges from the coupling of two twisted monolayers of superconducting Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ for certain twist angles. In this work, we reveal the behavior of such twisted…
The possibility of creating crystal bilayers twisted with respect to each other has led to the discovery of a wide range of novel electron correlated phenomena whose full understanding is still under debate. Here we propose and analyze a…
Topological photonics has recently been proved a robust framework for manipulating light. Active topological photonic systems, in particular, enable richer fundamental physics by employing nonlinear light-matter interactions, thereby…
Symmetry plays a critical role in classifying phases of matter. This is exemplified by how crystalline symmetries enrich the topological classification of materials and enable unconventional phenomena in topologically nontrivial ones. After…
Topological phases of matter have been extensively investigated in solid state materials and classical wave systems with integer dimensions. However, topological states in non-integer dimensions remain largely unexplored. Fractals, being…
We show that higher-order topological insulators can be created from usual square structure by twisting waveguides in each unit cell around the axis passing through the center of the unit cell, even without changing intracell distance…
Nonmagnetic topological insulators (TIs) are known for their robust metallic surface/edge states that are protected by time-reversal symmetry, making them promising candidates for next-generation spintronic and nanoelectronic devices.…
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…