Topological Charges, Fermi Arcs, and Surface States of $K_4$ Crystal

We investigate the topological electronic properties of the $K_4$ crystal by constructing a tight-binding model. The bulk band structure hosts Weyl nodes with higher and conventional chiralities ($\chi =\pm 2$ and $\chi =\pm 1$) located at high-symmetry points in the Brillouin zone. Through analytical evaluation of the Berry curvature, we identify the positions and chiralities of these Weyl nodes. Furthermore, slab calculations for the (001) surface reveal Fermi arcs that connect Weyl nodes of opposite chirality, including those linking $\chi =\pm 2$ nodes with pairs of $\chi =\mp 1$ nodes. These results demonstrate that the $K_4$ crystal is a spinless Weyl semimetal featuring topologically protected surface states originating from multiple types of Weyl nodes.