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Condensed Matter, Materials Science, Mathematics, Algebraic Topology
Abstract:
Screw rotations in nonsymmorphic space group symmetries induce the presence
of hourglass and accordion shape band structures along screw invariant lines
whenever spin-orbit coupling is nonnegligible. These structures induce
topological enforced Weyl points on the band intersections. In this work we
show that the chirality of each Weyl point is related to the representations of
the cyclic group on the bands that form the intersection. To achieve this, we
calculate the Picard group of isomorphism classes of complex line bundles over
the 2-dimensional sphere with cyclic group action, and we show how the
chirality (Chern number) relates to the eigenvalues of the rotation action on
the rotation invariant points. Then we write an explicit Hamiltonian endowed
with a cyclic action whose eigenfunctions restricted to a sphere realize the
equivariant line bundles described before. As a consequence of this relation,
we determine the chiralities of the nodal points appearing on the hourglass and
accordion shape structures on screw invariant lines of the nonsymmorphic
materials PI3 (SG: P63), Pd3N (SG: P6322), AgF3 (SG: P6122) and AuF3 (SG:
P6122), and we corroborate these results with the Berry curvature and symmetry
eigenvalues calculations for the electronic wavefunction.
