Electrostatic and magnetic confinement of electrons in graphene and in two dimensional Dirac materials like graphene

Firstly, in this thesis, some general properties of graphene are described and its electronic band structure was obtained by using the tight-binding model. The energy bands near the Fermi level, at the Dirac points, have a linear form leading to a Dirac – Weyl equation for the spectrum at low energies. Afterwards, supersymmetric quantum mechanics methods have been examined: factorization, Darboux transform, shape invariance and intertwining. The Pöschl – Teller potential is given as an example of shape invariance. Finally, solutions of the Dirac – Weyl equation describing the motions of Dirac fermions under the influence of electric and magnetic fields in graphene have been obtained for pure magnetic field, pure electric field and proportional electromagnetic field. Supersymmetric quantum mechanics methods have been used to find a solution to this problem.