  Metal atoms adsorbed on few layer graphenes condense to form nanometer-size
droplets whose growth is size limited by a competition between the surface
tension and repulsive electrostatic interactions from charge transfer between
the metal droplet and the graphene. For situations where the work function
mismatch is large and the droplet surface tension is small, a growing droplet
can be unstable to a family of shape instabilities. We observe this phenomenon
for Yb deposited and annealed on few layer graphenes and develop a theoretical
model to describe it by studying the renormalization of the line tension of a
two dimensional droplet by repulsive interparticle interactions. Our model
describes the onset of shape instabilities for nanoparticles where the growth
is size-limited by a generic repulsive potential and provides a good account of
the experimentally observed structures for Yb on graphene.
