Topological nodal line semimetals

TL;DR

This review summarizes recent theoretical advances in topological nodal line semimetals, focusing on their symmetry protection, topological invariants, material realizations, phase transitions, and experimental signatures.

Contribution

It provides a comprehensive classification of symmetry groups protecting nodal lines, explicit topological invariants, and discusses material proposals and phase transitions when symmetries are broken.

Findings

Classification of symmetry groups protecting nodal lines

Explicit topological invariants for different classes

Proposals for realizing these semimetals in materials

Abstract

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