Hourglass Dirac Chain Metal in Rhenium Dioxide

Nonsymmorphic symmetries, which involve fractional lattice translations in crystalline materials, can generate exotic types of fermionic excitations that are robust against spin-orbit coupling. Here we report on a hourglass-type dispersion in the bulk of three-dimensional rhenium dioxide crystals, as dictated by its nonsymmorphic symmetries. Due to time reversal and inversion symmetries, each band has an additional two-fold degeneracy, making the neck crossing-point of the hourglass four-fold degenerate. Remarkably, close to the Fermi level, the neck crossing-point traces out a Dirac chain--a chain of connected four-fold-degenerate Dirac loops--in the momentum space. The symmetry protection, the transformation under symmetry-breaking, and the associated topological surface states of the hourglass Dirac chain are discussed.