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In topological semimetals and nodal superconductors, band crossings betweenoccupied and unoccupied bands form stable nodal points/lines/surfaces carryingquantized topological charges. In particular, in centrosymmetric systems, somenodal structures at the Fermi energy $E_F$ carry two distinct topologicalcharges, and thus they are called doubly charged nodes. Here we show thatdoubly charged nodal surfaces of centrosymmetric superconductors inthree-dimensions always develop peculiar linking structures with nodal pointsor lines formed between occupied bands below $E_F$. Such linking structures cannaturally explain the inherent relationship between the charge of the nodebelow $E_F$ and the two charges of the nodal surfaces at $E_F$. Based on theAltland-Zirnbauer (AZ)-type ten-fold classification of nodes with additionalinversion $\mathcal{I}$ symmetry, which is called the AZ$+\mathcal{I}$classification, we provide the complete list of linking structures of doublycharged nodes in centrosymmetric systems. The linking structures of doublycharged nodes clearly demonstrate that not only the local band structure aroundthe node but also the global band structure play a critical role incharacterizing gapless topological phases.

Linking structures of doubly charged nodal surfaces in centrosymmetric superconductors