Coexistence of multifold and multidimensional topological phonons in KMgBO3

Hybrid single-pair charge-2 Weyl semimetals

“…The Weyl fermions are monopoles of Berry curvature in the Brillouin zone (BZ) and the charges associated with the monopoles are known as their chirality [11][12][13][14] . In crystalline materials, the Bloch function enriches the chiral charges to be ±1 [15][16][17][18][19][20][21] , ±2 [22][23][24][25][26][27][28] , ±3 29,30 , and even ±4 [31][32][33][34] , relying on the degree of degeneracy of the Weyl points and band dispersion around the Weyl nodes. In comparison with the conventional nodes [35][36][37][38][39] with the charges of ±1, the nodes with higher charge [40][41][42][43][44] are fascinating since the chiral charges determine the number of chiral edge states.…”

Hourglass Charge-Three Weyl Phonons

“…In 2012, Fang et al [22] demonstrated that with rotation symmetry, two (three) conventional WPs can merge together, leading to unconventional WP, which exhibits higher topological charge |C| = 2 (|C| = 3) and quadratic (cubic) dispersion in the plane normal to the rotation axis. This pioneering work led to a series of subsequent studies, such as the prediction of the corresponding material candidates [23][24][25][26][27][28][29][30], the demonstration of the novel phenomena of these unconventional WPs [31][32][33][34][35] and the search of other types of unconventional emergent particles [36][37][38][39][40]. Recently, one other species of the uncon-ventional WP, exhibiting topological charge |C| = 4, has been predicted in spinless nonmagnetic systems [41][42][43][44] and spinful magnetic systems [45].…”