In the last few years, much attention has been paid to the exotic properties that graphene
nanostructures exhibit, especially those emerging upon deforming the material. Here we present
a study of the mechanical and electronic properties of bent hexagonal graphene quantum dots
employing density functional theory. We explore three different kinds of surfaces with Gaussian
curvature exhibiting different shapes—spherical, cylindrical, and one-sheet hyperboloid—used to
bend the material, and several boundary conditions regarding what atoms are forced to lay on
the chosen surface. In each case, we study the curvature energy and two quantum regeneration
times (classic and revival) for different values of the curvature radius. A strong correlation between
Gaussian curvature and these regeneration times is found, and a special divergence is observed for
the revival time for the hyperboloid case, probably related to the pseudo-magnetic field generated by
this curvature being capable of causing a phase transition.
