The topological properties of electronic bands have received significant attention since the 1980s,and recently one of the most important progress in condensed matter systems is the discovery of the topological insulator (TI) [1].It had been found that insula-tors can be classified by a topological invariant that takes different values for TI and ordinary insulators [1],and the topological invari-ant cannot be changed without closing the energy gap of the sys-tem.Therefore usually people believe the gapless system cannot have interesting topological features.However,the band crossing points (BCPs) formed by two non-degenerate linearly dispersing energy bands can also be characterized by topological invariants and thus are robust against small perturbations [2].The excitation around such kind of BCPs can be described by the Weyl equation,and thus the system with them as the Fermi surface has been coined as Weyl semimetal (WSM) [2].WSM also hosts exotic Fermi arc surface states [2],and broadens the classification of topological phases of matter beyond insulators.Thus the topological features of various BCPs have attracted much attention [3-11].For example,by exploring the four-dimensional irreducible representations at high symmetry points (HSP) of Brillouin zone (BZ) [3] or high sym-metry lines (HSL) of BZ with different two-dimensional irreducible representations [4],three-dimensional Dirac semimetal had been proposed.Through the symmetry analysis,the linear and quadratic three-,six-,and eight-BCPs have been found,and the novel topo-logical properties have also been discussed [5].In addition to the zero-dimensional nodal points,the band crossing with different dimensionality has also been investigated and several topological matters,such as nodal line semimetals [6],nodal-chain metals[7],Hopf-link metals [8-10],hourglass fermions [11] have been proposed.

Xiangang Wan

National Laboratory of Solid State Microstructures and School of Physics,Nanjing University,Nanjing 210093,China;Collaborative Innovation Center of Advanced Microstructures,Nanjing University,Nanjing 210093,China

科学通报（英文版）

[1]Xiangang Wan-.A quasi-particle dictionary:exhaustive classification of energy band crossing in time-reversal-invariant systems)[J].科学通报（英文版）,2022(04):345-346

invari,BCPs

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