Topological semimetal driven by strong correlations and crystalline symmetry

Electron correlations amplify quantum fluctuations and, as such, they have been recognized the origin of a rich landscape phases. Whether and how lead to gapless topological states is an outstanding question, framework that allows for determining novel phases identifying new materials in pressing need. Here we advance general approach, which strong cooperate with crystalline symmetry drive states. We test this design principle by exploring Kondo lattice models whose space group symmetries may promote different kinds electronic degeneracies, particular focus on square-net systems. Weyl-Kondo nodal-line semimetals -- nodes pinned Fermi energy are identified. describe approach can be applied discover strongly correlated semimetals, identify three heavy fermion compounds candidates, provide first direct experimental evidence our prediction Ce$_2$Au$_3$In$_5$, discuss many more. Our findings illustrate potential proposed guide search metals broad range