Characterization of Lifshitz transitions in topological nodal line semimetals

TL;DR

This paper models three-dimensional nodal line semimetals, characterizes Lifshitz transitions between different Fermi surface topologies, and explores how additional terms can induce topological insulating phases with surface Dirac cones.

Contribution

Introduces a two-band model for nodal line semimetals, identifies Lifshitz transitions via gap-closing points, and studies the effects of spin-orbit coupling on topological phases.

Findings

Lifshitz transitions are characterized by the number of gap-closing points.

A global phase diagram of the model is constructed.

Extra terms can open gaps and lead to topological insulators with surface Dirac cones.

Abstract

We introduce a two-band model of three-dimensional nodal line semimetals, the Fermi surface of which at half-filling may form various one-dimensional configurations of different topology. We study the symmetries and "drumhead" surface states of the model, and find that the transitions between different configurations, namely, the Lifshitz transitions, can be identified solely by the number of gap-closing points on some high-symmetry planes in the Brillouin zone. A global phase diagram of this model is also obtained accordingly. We then investigate the effect of some extra terms analogous to a two-dimensional Rashba-type spin-orbit coupling. The introduced extra terms open a gap for the nodal line semimetals and can be useful in engineering different topological insulating phases. We demonstrate that the behavior of surface Dirac cones in the resulting insulating system has a clear correspondence with the different configurations of the original nodal lines in the absence of the gap terms.