Topological crystalline semimetals in non-symmorphic lattices

TL;DR

This paper identifies conditions under which non-symmorphic crystals with inversion and TRS host four-fold degenerate nodal line Fermi surfaces, and explores how breaking TRS leads to Dirac points or Weyl rings, with unique surface states.

Contribution

It provides a generic symmetry-based criterion for nodal line Fermi surfaces in non-symmorphic crystals with potential topological features.

Findings

Nodal line FS protected by non-symmorphic symmetries on BZ boundary.

Breaking TRS can lead to Dirac points or Weyl rings.

Existence of double helical surface states and Ferm arcs.

Abstract

Numerous efforts have been devoted to reveal exotic semimetallic phases with topologically non-trivial bulk and/or surface states in materials with strong spin-orbit coupling. In particular, semimetals with nodal line Fermi surface (FS) exhibit novel properties, and searching for candidate materials becomes an interesting research direction. Here we provide a generic condition for a four-fold degenerate nodal line FS in non-symmorphic crystals with inversion and time-reversal symmetry (TRS). When there are two glide planes or screw axes perpendicular to each other, a pair of Bloch bands related by non-symmorphic symmetry become degenerate on a Brillouin Zone (BZ) boundary. There are two pairs of such bands, and they disperse in a way that the partners of two pairs are exchanged on other BZ boundaries. This enforces a nodal line FS on a BZ boundary plane protected by non-symmorphic symmetries. When TRS is broken, four-fold degenerate Dirac points or Weyl ring FS could occur depending on a direction of the magnetic field. On a certain surface double helical surface states exist, which become double Ferm arcs as TRS is broken.