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Topological boundary modes utilizing valley mode waveguides have opened opportunities in, for instance, the design of high transmission waveguides with tolerance to geometrical defects and sharp bends. Applications of these waveguides…
The recent discovery and realizations of higher-order topological insulators enrich the fundamental studies on topological phases. Here, we report three-dimensional (3D) wave-steering capabilities enabled by topological boundary states at…
Bilayer graphene subjected to perpendicular magnetic and electric fields displays a subtle competition between different symmetry broken phases, resulting from an interplay between the internal spin and valley degrees of freedom. The…
Topological surface states, a new kind of electronic state of matter, have recently been observed on the cleaved surfaces of crystals of a handful of small band gap semiconductors. The underlying chemical factors that enable these states…
Moir\'e heterobilayer transition metal dichalcogenides (TMDs) emerge as an ideal system for simulating the single-band Hubbard model and interesting correlated phases have been observed in these systems. Nevertheless, the moir\'e bands in…
The recent discovery of higher-order topology has largely enriched the classification of topological materials. Theoretical and experimental studies have unveiled various higher-order topological insulators that exhibit topologically…
We show that moir\'e bands of twisted homobilayers can be topologically nontrivial, and illustrate the tendency by studying valence band states in $\pm K$ valleys of twisted bilayer transition metal dichalcogenides, in particular, bilayer…
Ideal Weyl points, which are related by symmetry and thus reside at the same frequency, could promote the deep development and utilization of the Weyl physics. Although the ideal type-I Weyl points have been achieved in photonic crystals,…
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…
We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only…
We identify the possibility of realizing higher order topological (HOT) phases in noncrystalline or amorphous materials. Starting from two and three dimensional crystalline HOT insulators, accommodating topological corner states, we…
Recent interest in optical analogues to the quantum spin Hall and quantum valley Hall effects is driven by the promise to establish topologically protected photonic edge modes at telecommunication and optical wavelengths on a simple…
We computer model a free-standing vitreous silica bilayer which has recently been synthesized and characterized experimentally in landmark work. Here we model the bilayer using a computer assembly procedure that starts from a single layer…
Using first principles methods, we investigate topological phase transitions as a function of exchange field in a Bi(111) bilayer. Evaluation of the spin Chern number for different magnitudes of the exchange field reveals that when the time…
Symmetry and topology are two fundamental aspects of many quantum states of matter. Recently, new topological materials, higher-order topological insulators, were discovered, featuring, e.g., bulk-edge-corner correspondence that goes beyond…
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…
Thanks to the recent discovery on the magic-angle bilayer graphene, twistronics is quickly becom11 ing a burgeoning field in condensed matter physics. This letter expands the realm of twistronics to acoustics by introducing twisted bilayer…
Recently, the higher-order topological phases from the chiral AIII symmetry classes are characterized by a Z topological invariant known as the multipole chiral numbers, which indicate the number of degenerate zero-energy corner states at…
We report on the design and experimental validation of a two-dimensional phononic elastic waveguide exhibiting topological Valley-Hall edge states. The lattice structure of the waveguide is inspired by the diatomic graphene and it is…
Square-root topological states are new topological phases, whose topological property is inherited from the square of the Hamiltonian. We realize the first-order and second-order square-root topological insulators in phononic crystals, by…