Eur. Phys. J. B (2018) 91: 75
https://doi.org/10.1140/epjb/e2018-80717-5

Regular Article

Characterization of Lifshitz transitions in topological nodal line semimetals

¹ Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, P.R. China
² School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P.R. China
³ Department of Physics, National University of Singapore, Singapore 117542, Singapore

^a e-mail: phylli@nus.edu.sg
^b e-mail: schen@iphy.ac.cn

Received: 20 December 2017
Published online: 2 May 2018

Abstract

We introduce a two-band model of three-dimensional nodal line semimetals (NLSMs), 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 NLSMs 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.