  Two-dimensional metals offer intriguing possibilities to explore metallicity
and other related properties in systems with reduced dimensionality. Here,
following recent experimental reports of synthesis of two-dimensional metallic
gallium (gallenene) on insulating substrates, we conduct a computational search
of gallenene structures using the Particle Swarm Optimization algorithm, and
identify stable low energy structures. Our calculations of the critical
temperature for conventional superconductivity yield values $\sim 7$ K for
gallenene. We also emulate the presence of the substrate by introducing the
external confining potential and test its effect on the structures with
unstable phonons.
