Fig. 3
Formation mechanism of hourglass Dirac chain. a Schematic figure of hourglass dispersion along a path on k x = π plane connecting R to any point P on U–X (including U). The labels indicate the \(\tilde {\cal M}_x\) eigenvalues. Partner switching between two quartets leads to the four-fold-degenerate crossing point (green dot). b, c Such crossing traces out Dirac loop b L 1 on k x = π plane, and also c L 2 on k z = π plane. The red-colored boundaries are the lines with four-fold band degeneracy. d, e Shape of two Dirac loops obtained from DFT. The color map indicates the local gap between two crossing bands
