摘要
Exotic links and chains attract interest across various disciplines including mathematics, biology, chemistry, and physics. Here, we propose that topological Hopf-chain networks, consisting of one-, two-, and three-dimensional (3D) Hopf chains, can be found in the momentum space. These networks can be evolved from a 3D triple-points phase by varying symmetries. Moreover, we identify that the Hopf-chain networks exist in a family of crystals Sc3XC (X = Al, Ga, In, T1). The crystals are 3D triple-points metals, and transit to topological metals with Hopf-chain networks under strains. These Hopf networks will exhibit unique magnetotransport properties.