Abstract
Despite recent efforts to advance spintronics devices and quantum information technology using materials with non-trivial topological properties, three key challenges are still unresolved1–9. First, the identification of topological band degeneracies that are generically rather than accidentally located at the Fermi level. Second, the ability to easily control such topological degeneracies. And third, the identification of generic topological degeneracies in large, multisheeted Fermi surfaces. By combining de Haas–van Alphen spectroscopy with density functional theory and band-topology calculations, here we show that the non-symmorphic symmetries10–17 in chiral, ferromagnetic manganese silicide (MnSi) generate nodal planes (NPs)11,12, which enforce topological protectorates (TPs) with substantial Berry curvatures at the intersection of the NPs with the Fermi surface (FS) regardless of the complexity of the FS. We predict that these TPs will be accompanied by sizeable Fermi arcs subject to the direction of the magnetization. Deriving the symmetry conditions underlying topological NPs, we show that the 1,651 magnetic space groups comprise 7 grey groups and 26 black-and-white groups with topological NPs, including the space group of ferromagnetic MnSi. Thus, the identification of symmetry-enforced TPs, which can be controlled with a magnetic field, on the FS of MnSi suggests the existence of similar properties—amenable for technological exploitation—in a large number of materials.
Highlights
Natural candidates are systems with non-symmorphic symmetries— for example, screw rotations—that generate positions in reciprocal space at which band-crossings are symmetry-enforced
The associated key characteristics include10–17: [1] the crossings are due to symmetry alone, that is, they occur on all bands independent of details such as chemical composition; [2] pairs of band crossings with opposite chirality are separated in k-space by about half a reciprocal lattice vector; [3] the band crossings may be enforced on entire planes11,12, forming so-called nodal planes (NPs) with non-zero topological charge; and [4] their existence may be controlled by means of symmetry breaking
Crystallizing in space group (SG) 198, manganese silicide (MnSi) is a magnetic sibling of non-magnetic RhSi, CoSi and PdGa, in which sizeable Fermi arcs and multifold fermions were recently inferred from angle-resolved photoemission spectroscopy
Summary
Natural candidates are systems with non-symmorphic symmetries— for example, screw rotations—that generate positions in reciprocal space at which band-crossings are symmetry-enforced. We note that besides the NPs, there is an odd number of symmetry-enforced band crossings on the Y1–Γ–Y and R1–U–R lines forming Weyl points (ν = ±1) and four-fold points (ν = ±2), respectively (Fig. 1c, d, Extended Data Fig. 2, Supplementary Note 1). As the sum over ν of all of these Weyl and four-fold points is odd, the duo of NPs must carry a non-zero topological charge to satisfy the fermion doubling theorem. By the bulk–boundary correspondence, the non-trivial topology of these band crossings generates large Fermi arcs on the surface, which extend over half of the BZ of the surface (Extended Data Fig. 4) These arguments may be extended to 254 of the 1,651 magnetic SGs, of which 33 have NPs whose topological charges are enforced to be non-zero by symmetry alone (Supplementary Note 3)
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