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Nodal loops in two-dimensional (2D) systems are typically vulnerable against spin-orbit coupling (SOC). Here, we explore 2D systems with a type of doubly degenerate nodal loops that are robust under SOC and feature an hourglass type…
Two-dimensional (2D) materials are frequently associated with the sheets which form bulk layered compounds bonded by van der Waals (vdW) forces. The anisotropy and weak interaction between the sheets have also been the main criteria in the…
Weyl points emerge as topological monopoles of Berry flux in the three-dimensional (3D) momentum space and have been extensively studied in topological semimetals. As the underlying topological principles apply to any type of waves under…
This perspective overviews the family of two-dimensional (2D) materials, which have attracted significant attention due to their properties and potential applications, and discusses how novel 2D materials including van der Waals (vdW) and…
Weyl fermions are hypothetical two-component massless relativistic particles in three-dimensional (3D) space, proposed by Hermann Weyl in 1929. Their band-crossing points, called 'Weyl points,' carry a topological charge and are therefore…
Phonon splitting of the longitudinal optical and transverse optical modes (LO-TO splitting), a ubiquitous phenomenon in three-dimensional (3D) polar materials, is essential for the formation of the 3D phonon polaritons. Theories predict…
Graphene as a two-dimensional (2D) topological Dirac semimetal has attracted much attention for its outstanding properties and potential applications. However, three-dimensional (3D) topological semimetals for carbon materials are still…
The topological metal states in electronic systems have been extensively studied, but topological phonons were explored only in few examples so far. Here, we expose for the first time that the topological nodal gimbal phonons, type-I and…
Weyl points, serving as monopoles in the momentum space and laying the foundation of topological gapless phases, have recently been experimentally demonstrated in various physical systems. However, none of the observed Weyl degeneracies are…
We propose a macroscopic theory of optical phonons, Fr{\"o}hlich polarons, and exciton-polarons in two-dimensional (2D) polar crystalline monolayers. Our theory extends the classical macroscopic formulation of the electron-phonon problem in…
In the \textsc{2-Dimensional Knapsack} problem (2DK) we are given a square knapsack and a collection of $n$ rectangular items with integer sizes and profits. Our goal is to find the most profitable subset of items that can be packed…
The Weyl modules in the sense of V.Chari and A.Pressley [CP] over the current Lie algebra on an affine variety are studied. We show that local Weyl modules are finite-dimensional and generalize the tensor product decomposition theorem from…
Phonons have provided an ideal platform for a variety of intriguing physical states, such as non-Abelian braiding and the Haldane model. It is promising that phonons will realize the complicated nodal states accompanying unusual quantum…
Extremely low-mass white dwarfs (ELM WDs) are helium-core white dwarfs with masses less than 0.3 $M_{\odot}$. Short-period ELM WD binaries that exhibit ellipsoidal variations may harbor heavier companions, either massive white dwarfs or…
Two-dimensional (2D) magnetic materials hosting nontrivial topological states are interesting for fundamental research as well as practical applications. Recently, the topological state of 2D Weyl half-semimetal (WHS) was proposed, which…
The study of Weyl points in electronic systems has inspired many recent researches in classical systems such as photonic and acoustic lattices. Here we show how the Weyl physics can also inspire the design of novel elastic structures. We…
Two dimensional (2D) materials have emerged as promising functional materials with many applications such as semiconductors and photovoltaics because of their unique optoelectronic properties. While several thousand 2D materials have been…
The hourglass fermions in solid-state materials have been attracting significant interest recently. However, realistic two-dimensional (2D) materials with hourglass-shaped band structures are still very scarce. Here, through the…
Soft materials can self-assemble into highly structured phases which replicate at the mesoscopic scale the symmetry of atomic crystals. As such, they offer an unparalleled platform to design mesostructured materials for light and sound.…
We present a real-space view of one-dimensional (1D) to three-dimensional (3D) topological materials with 13 representative samples selected from each class, including 1D trans-polyacetylene, two-dimensional (2D) graphene, and 3D…