Graphene nanostructures have attracted a lot of attention in recent years due to their
unconventional properties. We have employed Density Functional Theory to study the mechanical
and electronic properties of curved graphene nanoflakes. We explore hexagonal flakes relaxed with
different boundary conditions: (i) all atoms on a perfect spherical sector, (ii) only border atoms forced
to be on the spherical sector, and (iii) only vertex atoms forced to be on the spherical sector. For
each case, we have analysed the behaviour of curvature energy and of quantum regeneration times
(classical and revival) as the spherical sector radius changes. Revival time presents in one case a
divergence usually associated with a phase transition, probably caused by the pseudomagnetic field
created by the curvature. This could be the first case of a phase transition in graphene nanostructures
without the presence of external electric or magnetic fields.
