Topological nodal line semimetals

Abstract

We review the recent, mainly theoretical, progress in the study of\ntopological nodal line semimetals in three dimensions. In these semimetals, the\nconduction and the valence bands cross each other along a one-dimensional curve\nin the three-dimensional Brillouin zone, and any perturbation that preserves a\ncertain symmetry group (generated by either spatial symmetries or time-reversal\nsymmetry) cannot remove this crossing line and open a full direct gap between\nthe two bands. The nodal line(s) is hence topologically protected by the\nsymmetry group, and can be associated with a topological invariant. In this\nReview, (i) we enumerate the symmetry groups that may protect a topological\nnodal line; (ii) we write down the explicit form of the topological invariant\nfor each of these symmetry groups in terms of the wave functions on the Fermi\nsurface, establishing a topological classification; (iii) for certain classes,\nwe review the proposals for the realization of these semimetals in real\nmaterials and (iv) we discuss different scenarios that when the protecting\nsymmetry is broken, how a topological nodal line semimetal becomes Weyl\nsemimetals, Dirac semimetals and other topological phases and (v) we discuss\nthe possible physical effects accessible to experimental probes in these\nmaterials.\n