Fig. 1

Dirac chain and hourglass dispersion. a Schematic figure showing Dirac chain in ReO2, which consists of one (red) loop in k z = π plane and one (green) loop in k x = π plane. There is another isolated Dirac point (orange dot) on T–Y. These crossings are four-fold degenerate and correspond to the neck crossing-point of the hourglass-type dispersion. For example, b shows the schematic band dispersion along a path on the k x = π plane connecting R and P (an arbitrary point on U–X). Each band is two-fold degenerate, and the neck point (green dot) is four-fold degenerate