Topological and superconducting properties in bilayer kagome metals YT6Sn6 ( T =V, Nb, Ta)

Kagome materials exhibit fascinating properties and hold important research significance. Inspired by the extensive studies on the $A{\mathrm{V}}_{3}{\mathrm{Sb}}_{5}$ family of materials, here, we investigate the topological and superconducting properties of the bilayer kagome metal materials $\mathrm{Y}{T}_{6}{\mathrm{Sn}}_{6}$ ($T$=V, Nb, Ta) using first-principles calculations. These kagome materials exhibit the ${\mathrm{MgFe}}_{6}{\mathrm{Ge}}_{6}$-prototype structure and have no magnetism. The calculated results for formation energy and the phonon dispersion spectrum demonstrate their stability. Based on the calculation of topologically invariant and surface states, they can be categorized as ${\mathbb{Z}}_{2}$ topological metals. The Van Hove singularity and Dirac points are also observed near the Fermi level. According to electron-phonon coupling (EPC) calculations, $\mathrm{Y}{T}_{6}{\mathrm{Sn}}_{6}$ systems are all predicted to be weak superconductors. Using the Allen-Dynes modified McMillan formula, the superconducting critical temperatures ${T}_{c}$ of ${\mathrm{YV}}_{6}{\mathrm{Sn}}_{6}, {\mathrm{YNb}}_{6}{\mathrm{Sn}}_{6}$, and ${\mathrm{YTa}}_{6}{\mathrm{Sn}}_{6}$ are predicted to be 0.65, 1.17, and 0.89 K, respectively. The EPC is mainly contributed by the vibrations of V atoms and partially by the out-of-plane vibrational modes of Sn atoms. The coexistence of nontrivial topological properties and superconducting properties in these bilayer kagome systems is helpful to study the relationship between different physical properties and to design new topological superconductors.