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Topological semimetals, such as the Weyl and Dirac semimetals, represent one of the most active research fields in modern condensed matter physics. The peculiar physical properties of these systems mainly originate from their underlying…
A method is introduced to analyze the degeneracy properties of the band structure of a photonic crystal making use of the super cells. The band structure associated with a super cell of a photonic crystal has degeneracies at the edge of the…
Non-Abelian topological phases (NATPs) are highly sought-after candidate states for quantum computing and communication while lacking straightforward configuration and manipulation, especially for classical waves. In this work, we exploit…
Based on the first-principles study, we report a new set of topological semimetals (TiS, TiSe, TiTe, HfS, HfSe, HfTe and ZrS) which show the co-existence of a nodal-ring and triply-degenerate points. The two-fold degenerate one-dimensional…
Combining strong electron correlations [1-4] and nontrivial electronic topology [5] holds great promise for discovery. So far, this regime has been rarely accessed and systematic studies are much needed to advance the field. Here we…
Topological semimetals are three dimensional materials with symmetry-protected massless bulk excitations. As a special case, Weyl nodal-line semimetals are realized in materials either having no inversion or broken time-reversal symmetry…
The exploration of topological phase transition (TPT) mechanisms constitutes a central theme in quantum materials research. Conventionally, transitions between Weyl semimetals (WSMs) and other topological states rely on the breaking of…
Classical topological phases derived from point degeneracies in photonic bandstructures show intriguing and unique behaviour. Previously identified exceptional points are based on accidental degeneracies and subject to engineering on a…
Crystalline semimetals with certain space group symmetries may possess unusual electronic structure topology, distinct from the conventional Weyl and Dirac semimetals. Characteristic property of these materials is the existence of…
Weyl semimetals are phases of matter with gapless electronic excitations that are protected by topology and symmetry. Their properties depend on the dimensions of the systems. It has been theoretically demonstrated that five-dimensional…
A pair of Weyl points (WPs) with opposite Chern numbers ${\cal{C}}$ can exhibit an additional higher-order $Z_2$ topological charge, giving rise to the formation of a $Z_2$ Weyl dipole. Owing to the nontrivial topological charge, $Z_2$ Weyl…
Altermagnets constitute a novel, third fundamental class of collinear magnetic ordered materials, alongside with ferro- and antiferromagnets. They share with conventional antiferromagnets the feature of a vanishing net magnetization. At the…
Topological photonic crystals have received considerable attention for their ability to manipulate and guide light in unique ways. They are typically designed by hand based on careful analysis of their bands and mode profiles, but recent…
We consider an example of a system with two degrees of freedom admitting separation of variables but having a subset of codimension 1 on which the 2-form defining the symplectic structure degenerates. We show how to use separation of…
Exceptional points (EPs) are non-Hermitian degeneracies where eigenvalues and eigenvectors coalesce, giving rise to unusual physical effects across scientific disciplines. The concept of EPs has recently been extended to nonlinear physical…
We challenge the hypothesis that the ground states of a physical system whose degeneracy depends on topology must necessarily realize topological quantum order and display non-local entanglement. To this end, we introduce and study a…
Crystalline topological phases have recently attracted a lot of experimental and theoretical attention. Key advances include the complete elementary band representation analyses of crystalline matter by symmetry indicators and the discovery…
Non-Abelian topological charges (NATCs), characterized by their noncommutative algebra, offer a framework for describing multigap topological phases beyond conventional Abelian invariants. While higher-order topological phases (HOTPs) host…
It is well-known that many topological phase transitions of intrinsic Abelian topological phases are accompanied by condensation and confinement of anyons. However, for non-Abelian topological phases, more intricate phenomena can occur at…
Unconventional Weyl point with nonlinear dispersion features higher topological charge $|{\cal{C}}|>1$ and multiple topologically protected Fermi arc states at its boundary. As a novel topological state, it has been attracting widespread…