Parallel and anti-parallel helical surface states for topological semimetals

TL;DR

This paper reviews the complex surface states in topological semimetals, focusing on parallel and anti-parallel helical surface states associated with different monopole charges, and discusses their topological properties and material examples.

Contribution

It systematically analyzes both parallel and anti-parallel multi-helical surface states in Weyl and Dirac semimetals with different monopole charges, providing new insights into their topological configurations.

Findings

Identification of local and global topology in Weyl points with Z-type charge C.

Discovery of anti-parallel multi-HSSs associated with Z2 monopole charge Q.

Material examples illustrating diverse topological surface state configurations.

Abstract

Weyl points, carrying a Z-type monopole charge C, have bulk-surface correspondence (BSC) associated with helical surface states (HSSs). When |C| > 1, multi-HSSs can appear in a parallel manner. However, when a pair of Weyl points carrying C = \pm 1 meet, a Dirac point carrying C = 0 can be obtained and the BSC vanishes. Nonetheless, a recent study in Ref. [arXiv:2201.03238] shows that a new BSC can survive for Dirac points when the system has time-reversal (T )-glide (G) symmetry ({\Theta}=TG), i.e., anti-parallel double/quad-HSSs associated with a new Z2-type monopole charge Q appears. In this paper, we systematically review and discuss both the parallel and anti-parallel multi-HSSs for Weyl and Dirac points, carrying two different kinds of monopole charges. Two material examples are offered to understand the whole configuration of multi-HSSs. One carries the Z-type monopole charge C, shows both local and global topology for three kinds of Weyl points, and it leads to parallel multi-HSSs. The other carries the Z2-type monopole charge Q, only showing the global topology for {\Theta}-invariant Dirac points, and it is accompanied by antiparallel multi-HSSs. These diverse topological surface states not only offer the local and global topology for the bulk degeneracy but also offer platforms to various topological phases.