Topological semimetals, topological phase transitions, and candidate materials

In this talk, we focus on topological semimetals and associated novel properties and discuss candidate materials. The simplest topological semimetal is the Weyl semimetal [1]. The Weyl semimetal often appears as an intermediate phase between different topological phases [2], and we show the band-gap closing is directly related to a change in the topological invariants [1-3]. Such a band-gap closing is accompanied by a polarization jump, and this jump is directly written by a "Weyl dipole" [4].

Furthermore, among various properties of topological semimetals, we are recently focusing on an interplay between various topological degeneracies, such as Weyl points and nodal lines [5,6]. In particular, we introduce our work on the multi-helicoid surface states associated with Dirac points. Here we find that the Z2 topological invariant for the Dirac point in the previous work should be redefined and that it is eventually equal to the Z2 topological invariant for the glide-symmetric TCI. With this redefined Z2 topological invariant, we show the bulk-edge correspondence for the double/quad-helicoid surface states. Candidate materials for the multi-helicoid surface states are also discussed [5].

If time allows, we also briefly discuss our recent works on the fractional corner charges of three-dimensional obstructed atomic insulators with crystal shapes being vertex-transitive polyhedra [7,8], and on anomalous crystal shapes in topological insulators [9].