Type-II nodal line fermions in the Z2 topological semimetals AV6Sb6 (

The recently discovered layered kagome metals $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ ($A$=K, Rb, and Cs) attract intensive interest due to their intertwining with superconductivity, charge-density-wave state, and nontrivial band topology. In this work, we show by first-principles calculations and symmetry arguments that unconventional type-II Dirac nodal line fermions close to the Fermi level are present in another latest class of experimentally synthesized kagome compounds $A{\mathrm{V}}_{6}{\mathrm{Sb}}_{6}$ ($A$=K, Rb, and Cs). These compounds possess a unique kagome ${({\mathrm{V}}_{3}\mathrm{Sb})}_{2}$ bilayer that dominates their electronic and topological properties, instead of the kagome ${\mathrm{V}}_{3}\mathrm{Sb}$ monolayer in $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$. Crystal symmetry guarantees that the type-II Dirac nodal lines with quantized Berry phase lie in reflection-invariant planes of the Brillouin zone. We further reveal that the type-II Dirac nodal lines remain nearly intact in the presence of spin-orbital coupling and can be categorized as a ${\mathbb{Z}}_{2}$ classification. The findings establish $A{\mathrm{V}}_{6}{\mathrm{Sb}}_{6}$ as a class of new fascinating prototypes, which will extend the knowledge of interplay between unconventionally topological fermions and exotic quantum ordered states in kagome systems.