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Classification of materials is important to predict new materials and
phenomena, as the periodic table of elements. We give a classification
of topological nodal-line semimetals which enables us to predict new
topological materials including topological insulators and Dirac
semimetals without any detailed calculation. Topological semimetals, in
which the band gap closes on some points, lines, or surfaces, exhibits
exotic quantum phenomena. Such phenomena depend on the configuration of
nodes of the band gap. Indeed, line nodes can show a peculiar
electromagnetic response; finite electric polarization and orbital
magnetization under an infinitesimal external field, as in
ferroelectrics and ferromagnets. Differently from point nodes, line
nodes possibly form various structures such as spirals, chains, and
multiple crossing rings, as shown in Figs(a)-(e). Therefore, we expect
rich behaviors of electromagnetic responses inherent to line nodes.
Towards the realization of them, in this study, we classify possible
configurations of line nodes and give an example, rare-earth
trihydrides. We believe that with the help of our theory many
researchers can discover new topological materials and will reveal
topological electromagnetic responses.
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