Two topologically distinct Dirac-line semimetal phases and topological phase transitions in rhombohedrally stacked honeycomb lattices

TL;DR

This paper explores topologically distinct Dirac-line semimetal phases in rhombohedrally stacked honeycomb lattices, revealing how tuning tunneling parameters induces phase transitions between different topological states with unique surface properties.

Contribution

It identifies two topologically distinct Dirac-line phases in rhombohedral honeycomb lattices and describes how to transition between them by tuning tunneling amplitudes.

Findings

Existence of two topologically distinct Dirac-line phases.

Topological phase transition occurs by merging and shrinking Dirac lines.

Surface states differ between the phases.

Abstract

Three-dimensional topological semimetals can support band crossings along one-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 by time-reversal, inversion and spin rotation symmetries. For typical band structure parameters there exists a pair of nodal lines in the momentum space extending through the whole Brillouin zone in the stacking direction. We show that these Dirac lines are topologically distinct from the usual Dirac lines which form closed loops inside the Brillouin zone. In particular, an energy gap can be opened only by first merging the Dirac lines going through the Brillouin zone in a pairwise manner so that they turn into closed loops inside the Brillouin zone, and then by shrinking these loops into points. We show that this kind of topological phase transition can occur in rhombohedrally stacked honeycomb lattices by tuning the ratio of the tunneling amplitudes in the directions perpendicular and parallel to the layers. We also discuss the properties of the surface states in the different phases of the model.