We consider a two-orbital tight-binding model defined on a layered three-dimensional hexagonal lattice to investigate the properties of topological nodal lines and their associated drumhead surface states. We examine these surface states in centrosymmetric systems, where the bulk nodal lines are of Dirac type (i.e., four-fold degenerate), as well as in non-centrosymmetric systems with strong Rashba and/or Dresselhaus spin-orbit coupling, where the bulk nodal lines are of Weyl type (i.e., two-fold degenerate). We find that in non-centrosymmetric systems the nodal lines and their corresponding drumhead surface states are fully spin polarized due to spin-orbit coupling. We show that unique signatures of the topologically nontrivial drumhead surface states can be measured by means of quasiparticle scattering interference, which we compute for both Dirac and Weyl nodal line semimetals. At the end, we analyze the possible crystal structures with a symmetry that supports flat surface states which are effectively ringlike.
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