Local and global topology for Dirac points with multihelicoid surface states
 Date
 March 24 (Thu) at 17:00  18:15, 2022 (JST)
 Speaker

 Tiantian Zhang (Specially Appointed Assistant Professor, School of Science, Tokyo Institute of Technology)
 Venue
 via Zoom
 Language
 English
Though topological invariants defined for topological semimetals are usually local ones, they also have a global nature. For example, the Z type local monopole charge C for Weyl points, has a global nature, telling us its influence to the rest of the Brillouin zone, giving rise to bulksurface correspondence associated with helical surface states. In Dirac systems, helical surface states are not guaranteed due to C=0. However, a new bulksurface correspondence associated with double/quadhelicoid surface states (DHSSs/QHSSs) can be obtained for Dirac points with the protection of a Z2 type monopole charge Q, which is defined in terms of the timereversal (T)glide (G) symmetry (TG)2= 1. Here we study the topology of Q for Z2 Dirac points and establish its bulksurface correspondence with strict proofs. We find that Q is equivalent to the Gprotected Z2 invariant v mathematically and physically in Z2 Dirac systems. This result is counterintuitive, since v is always trivial in Tpreserving gapped systems, and was thought to be illdefined in gapless systems. We offer a gaugeinvariant formula for Q, which is associated with DHSSs in both the spinless and spinful systems with single G. Q is formulated in a simpler form in spinless systems with two vertical G, associated with QHSSs, which is also entangled with fillingenforced topological band insulators in three space groups when a Tbreaking perturbation is introduced. Since Q is illdefined in spinful systems with two vertical G, QHSSs will not be held. Material candidate Li2B4O7 together with a list of possible space groups preserving QHSSs are also proposed for demonstration on our theory and further studies.
*Detailed information about the seminar refer to the email.