Topological Semimetals & beyond

Topological semimetals in three dimensions are of mainly two variants, with the bands touching at point nodes (Weyl or Dirac semimetals) or at nodal lines in the Brillouin zone. However, there are new semimetals, namely Nexus semimetals, that challenge our notion. I will explain when they can occur and why their classification breaks our usual analysis via topological insulators. I will also describe what we can learn from them. I will explain a new topological invariant that will help us to understand the nexus topology. This also has some more applications, e.g. fragile topology, that I will also talk about. After that, I hope to briefly discuss the topological Nodal line semimetals in 3D. I will provide argument that chiral symmetry classes, which are topologically nontrivial in three dimensions (namely class AIII, CII, DIII, and CI) always have a stable gapless phase. Even for a minimal model, this gapless phase is a topological nodal line 
semimetal.

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Ref: PRB 102, 235148 (2020); PRL 130, 186202 (2023); arXiv: 2309.xxx
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