Topological Nodal Line Semimetals with Chiral Symmetry*

Topological semimetals occur in two variants, with the bands touching at point nodes (Weyl or Dirac semimetals), or touching at nodal lines in the Brillouin zone. While Weyl/Dirac semimetals can occur with internal symmetries only (such as time-reversal, charge conjugation, and possibly a product of the two, called chiral/sublattice symmetry), nodal line semimetals have been believed to require more symmetry, such as SU(2) spin rotation or crystalline symmetries. Here we show that in the presence of chiral symmetry, additional symmetries are not necessary to have topological nodal line semimetals. Starting from a generic model Hamiltonian possessing only time-reversal, inversion, and chiral symmetries, which belongs to the Altland-Zirnbauer symmetry class CII, we demonstrate how a topological nodal line semimetal can be obtained by breaking either time-reversal, inversion symmetry, or both. The nodal line semimetal has robust topological surface states protected by chiral symmetry. Our findings will be useful for ongoing explorations of topological nodal line semimetals.