Three-dimensional topological semimetals can support band crossings alongone-dimensional curves in the momentum space (nodal lines or Dirac lines)protected by structural symmetries and topology. We consider rhombohedrally(ABC) stacked honeycomb lattices supporting Dirac lines protected bytime-reversal, inversion and spin rotation symmetries. For typical bandstructure parameters there exists a pair of nodal lines in the momentum spaceextending through the whole Brillouin zone in the stacking direction. We showthat these Dirac lines are topologically distinct from the usual Dirac lineswhich form closed loops inside the Brillouin zone. In particular, an energy gapcan be opened only by first merging the Dirac lines going through the Brillouinzone in a pairwise manner so that they turn into closed loops inside theBrillouin zone, and then by shrinking these loops into points. We show thatthis kind of topological phase transition can occur in rhombohedrally stackedhoneycomb lattices by tuning the ratio of the tunneling amplitudes in thedirections perpendicular and parallel to the layers. We also discuss theproperties of the surface states in the different phases of the model.
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