Charge-six twofold Weyl states induced by the coupling of neighboring bands

Crystal symmetry has long been regarded as a crucial factor in generating various topological quasiparticle states. Constrained by all possible symmetries in materials, the Chern number $\mathcal{C}$ of a twofold Weyl point (WP) is believed to have a maximum value of $|\mathcal{C}|=4$. In this study, we discover that when considering the coupling between two quadratic crossing bands and their neighboring bands in momentum space, the crossing point may transform into a twofold quadratic WP. Due to its partial crystal symmetry constraint, the Chern number of this twofold WP surpasses the maximum Chern number constraint, attaining a value of $|\mathcal{C}|=6$. Its pseudospin structure differs from those of all previously reported WPs and the sextuple-helicoid surface arc state is well produced, thereby firmly confirming its nontrivial topological nature. Notably, this twofold WP with $|\mathcal{C}|=6$ is well established in an acoustic crystal in space group no. 168. Our theoretical discovery paves another way for exploring unconventional topological phenomena.