  While the growth of germanene has been claimed on many substrates, the exact
crystal structures remain controversial. Here, we systematically explore the
possible structures formed by Ge deposition onto Al(111) surface by combining
density-functional theory (DFT) and global optimization algorithm. We show
that, by high-level random-phase approximation (RPA) calculations, the
formation of germanene on Al(111) is energetically unfavorable with positive
formation energy. The two experimental phases are identified as honeycomb
alloys Al3Ge3/Al(111)(r7xr7) and Al3Ge4/Al(111)(3x3), by combining ab initio
evolutionary simulations, RPA calculations, and available experimental data
from scanning tunneling microscopy (STM) and low-energy electron diffraction
(LEED). Al3Ge4/Al(111)(3x3) is an interesting structure with a vacancy in the
substrate, which accounts for the dark clover pattern in the experimental STM
image. Our results clarify the structural controversy of the Ge/Al(111) system
and indicate the fabrication of germanene may remain challenging.
