Abstract We provide an updated study of some electronic properties graphene nanoscrolls, exploiting a related curved space Dirac equation for the charge carriers. To this end, we consider explicit parametrization in cylindrical coordinates, together with analytical solutions pseudoparticle modes living on two–dimensional background. These results are then used to obtain compact expression sampl...

We consider the Dirac equation in the magnetic-solenoid field (the field of a solenoid and a collinear uniform magnetic field). For the case of Aharonov-Bohm solenoid, we construct self-adjoint extensions of the Dirac Hamiltonian using von Neumann’s theory of deficiency indices. We find self-adjoint extensions of the Dirac Hamiltonian and boundary conditions at the AB solenoid. Besides, for the...