Pseudo-magnetic fields of strongly-curved graphene nanobubbles

We use the π-orbital axis vector (POAV) analysis to deal with large curvature effect of graphene in the tight-binding model. To test the validities of pseudo-magnetic fields (PMFs) derived from the tight-binding model and the model with Dirac equation coupled to a curved surface, we propose two types of spatially constant-field topographies for strongly-curved graphene nanobubbles, which correspond to these two models, respectively. It is shown from the latter model that the PMF induced by any spherical graphene nanobubble is always equivalent to the magnetic field caused by one magnetic monopole charge distributed on a complete spherical surface with the same radius. Such a PMF might be attributed to the isometry breaking of a graphene layer attached conformably to a spherical substrate with adhesion.