Favored configurations for four-quasiparticle K isomerism in the heaviest nuclei

Configuration-constrained potential-energy-surface calculations are performed including ${\ensuremath{\beta}}_{6}$ deformation to investigate high-$K$ isomeric states in nuclei around ${}^{254}$No and ${}^{270}$Ds, the heaviest nuclei where there have been some observations of two-quasiparticle isomers, while data for four-quasiparticle isomers are scarce. We predict the prevalent occurrence of four-quasiparticle isomeric states in these nuclei, together with their favored configurations. The most notable examples, among others, are ${K}^{\ensuremath{\pi}}={20}^{+}$ states in ${}^{266,268}$Ds and ${}^{268,270}$Cn having very high $K$ value, relatively low excitation energy, and well-deformed axially symmetric shape. The predicted isomeric states, with hindered spontaneous fission and $\ensuremath{\alpha}$ decay, could play a significant role in the future study of superheavy nuclei.