In this paper, it has been shown that A_5 and PSL (2,7) are the only simple groups which just contain 15 or 21 in volutions, respectively. Meanwhile, we have also obtained some results about finite CIT-groups and fini...In this paper, it has been shown that A_5 and PSL (2,7) are the only simple groups which just contain 15 or 21 in volutions, respectively. Meanwhile, we have also obtained some results about finite CIT-groups and finite nonsolvabie CIT-groups.展开更多
In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron＇s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 （P212121 ）...In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron＇s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 （P212121 ） and No. 198 （P213）, which have three orthogonal screw rotation axes. In the case of space groups No. 61 （Pbca） and No. 205 （Pa-3） that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respectively, to appear along its rotation axes in the Brillouin zone and generates four-fold and six-fold degeneracy at the F point and R point, respectively.展开更多
文摘In this paper, it has been shown that A_5 and PSL (2,7) are the only simple groups which just contain 15 or 21 in volutions, respectively. Meanwhile, we have also obtained some results about finite CIT-groups and finite nonsolvabie CIT-groups.
基金supported by JSPS Kakenhi(No.15K05141)from Japan Society for the Promotion of Science
文摘In three-dimensional noncentrosymmetric materials two-fold screw rotation symmetry forces electron＇s energy bands to have Weyl points at which two bands touch. This is illustrated for space groups No. 19 （P212121 ） and No. 198 （P213）, which have three orthogonal screw rotation axes. In the case of space groups No. 61 （Pbca） and No. 205 （Pa-3） that have extra inversion symmetry, Weyl points are promoted to four-fold degenerate line nodes in glide-invariant planes. The three-fold rotation symmetry present in the space groups No. 198 and No. 205 allows Weyl and Dirac points, respectively, to appear along its rotation axes in the Brillouin zone and generates four-fold and six-fold degeneracy at the F point and R point, respectively.
