First-principles prediction of symmetry-enforced multifold fermionic and bosonic degeneracies in M3Sn (M = V, Nb) compounds

Topological quantum materials featuring multifold band crossings have opened unprecedented pathways in the exploration of exotic matter phases. These multifold crossings with three-, six-, and eightfold degeneracies hold exceptional significance, as they are ruled out in high-energy frameworks by Poincaré symmetry, making their realization in solids highly nontrivial. Notably, the coexistence of higher-fold fermionic (eightfold) and bosonic (sixfold) degeneracies in a single material is scarcely observed in literature. In this regard, we conducted a detailed investigation into the symmetry-protected topological characteristics of experimentally synthesized A15-type M3Sn (M = V, Nb) compounds using first-principles calculations. Our scrutiny unveils sixfold degeneracies in M3Sn compounds, which corresponds to the maximum allowed in bosonic systems along with threefold nodal points, while an eightfold and fourfold fermionic degeneracy are identified in V3Sn compound at the R-high-symmetry point protected by nonsymmorphic crystalline symmetry. The phonon and electronic surface states calculated from a tight-binding model further validate the multifold degeneracies and also represent complementary Dirac surface states at the Γ-point. The phononic Weyl nodal line along the Γ–R path exhibits nontrivial topology with ±π Berry phase. The synthesized compounds have been confirmed to theoretically exhibit both dynamic and thermal stabilities. Our findings offer a promising platform to explore exotic excitations within a single material, paving the way for deeper insights into complex quasiparticle behavior in these potential superconductors.