Nodal lines in momentum space: topological invariants and recent realizations in photonic and other systems

TL;DR

This paper reviews the theoretical and experimental progress on topological nodal lines in momentum space, highlighting their properties, recent realizations in artificial systems, and ongoing challenges in understanding and demonstration.

Contribution

It provides a comprehensive overview of the topological properties of nodal lines and recent advances in their realization in photonic and other artificial systems.

Findings

Demonstration of non-Abelian topological charges of nodal lines

Realizations of nodal lines in photonic and other systems

Discussion of challenges in experimental and theoretical understanding

Abstract

Topological insulators constitute one of the most intriguing phenomena in modern condensed matter theory. The unique and exotic properties of topological states of matter allow for unidirectional gapless electron transport and extremely accurate measurements of the Hall conductivity. Recently, new topological effects occurring at Dirac/Weyl points have been better understood and demonstrated using artificial materials such as photonic and phononic crystals, metamaterials and electrical circuits. In comparison, the topological properties of nodal lines, which are one-dimensional degeneracies in momentum space, remain less explored. Here, we explain the theoretical concept of topological nodal lines and review recent and ongoing progress using artificial materials. The review includes recent demonstrations of non-Abelian topological charges of nodal lines in momentum space and examples of nodal lines realized in photonic and other systems. Finally, we will address the challenges involved in both experimental demonstration and theoretical understanding of topological nodal lines.