Nonmonotonic superconductivity, nontrivial band topology, and electride state in a beryllene system

Controlling the layer number of superconducting (SC) units can effectively modulate superconductivity of layered materials. Here, through first-principles calculations, the electronic and SC properties of beryllenes have been systematically investigated. The SC transition temperature ${T}_{c}$ shows nonmonotonic behavior, with maximum of 8.5 K for AB-stacking and 6.4 K for ABC-stacking trilayer beryllenes. Notably, these ${T}_{c}$ are two orders of magnitude higher than 0.026 K of bulk beryllium attributed to the enhanced electron-phonon coupling from phonon softening of surface Be and the increased density of states at the Fermi level. Additionally, several beryllenes exhibit nontrivial band topology, providing platforms for studying topological superconductivity. Moreover, all the beryllenes show the electride nature due to interstitial anionic electrons. These results highlight the importance of reduced dimensionality on physical properties and offer the first example of a single-element material with trilayer SC units achieving the highest ${T}_{c}$.