Dirac and Weyl materials with nodal lines

Dirac and Weyl electrons in topological semimetals potentially show exotic electromagnetic responses, while it has not been experimentally discovered yet. For further development, we have proposed ideal candidate materials of nodal-line semimetals, CaAgX(X=P,As) [A. Yamakage et al., J. Phys. Soc. Jpn. 85, 013708 (2016); Y. Okamoto and A. Yamakage et al., J. Phys. Soc. Jpn. 85, 123701 (2016); D. Takane and A. Yamakage et al., arXiv:1708.06874] and RH₃(R: rare earth) [S. Kobayashi and A. Yamakage et al., Phys. Rev. B 95, 245208 (2017)] that host simple electronic states with torus Fermi surface (line nodes) and without other conventional Fermi surfaces. And spin-nondegenerate nodal lines, which appear in PbTaSe₂, for instance, are also interesting topological electronic states which can lead to (quasi) topological electromagnetic response such as electric polarization induced by an infinitesimal electric field [S. T. Ramamurthy and T. L. Hughes, Phys. Rev. B 95, 075138 (2017)]. We propose a toy model in which only Weyl nodal lines form the Fermi surface and discuss a building block for Weyl nodal lines and the presence/absence of spin-split drumhead surface states.