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Topological semimetals have energy bands near the Fermi energy stickingtogether at isolated points/lines/planes in the momentum space, which are oftenaccompanied by stable surface states and intriguing bulk topological responses.Although it has been known that certain crystalline symmetries play animportant role in protecting band degeneracy, a general recipe for stabilizingthe degeneracy, especially in the presence of spin-orbit coupling, is stilllacking. Here we show that a class of novel topological semimetals withpoint/line nodes can emerge in the presence of an off-centered rotation/mirrorsymmetry whose symmetry line/plane is displaced from the center of othersymmorphic symmetries in nonsymmorphic crystals. Due to the partial translationperpendicular to the rotation axis/mirror plane, an off-centeredrotation/mirror symmetry always forces two energy bands to stick together andform a doublet pair in the relevant invariant line/plane in momentum space.Such a doublet pair provides a basic building block for emerging topologicalsemimetals with point/line nodes in systems with strong spin-orbit coupling.

Topological semimetals protected by off-centered symmetries in nonsymmorphic crystals