Nodal-chain network, intersecting nodal rings and triple points coexisting in nonsymmorphic Ba₃Si₄

Coexistence of topological elements in topological metals/semimetals (TMs) has gradually attracted attention. However, non-topological factors always interfere with the Fermi surface and cover interesting topological properties. Here, we find that Ba3Si4 is a "clean" TM which contains coexisting nodal-chain networks, intersecting nodal rings (INRs) and triple points, in the absence of spin-orbit coupling (SOC). Moreover, the nodal rings in the topological phase exhibit diverse types: from type-I and type-II to type-III rings according to band dispersions. All of the topological elements are generated by crossings of three energy bands, and thus they are correlated rather than mutually independent. When some structural symmetries are eliminated by an external strain, the topological phase evolves into another phase including a Hopf link, a one-dimensional nodal chain and new INRs.