The extension of the massless fermion in the cosmic string spacetime

In this work, we have obtained the solutions of a massless fermion which is under the external magnetic field around a cosmic string for specific three potential models using supersymmetric quantum mechanics. The constant magnetic field, energy dependent potentials and position dependent mass models are investigated for the Dirac Hamiltonians and an extension of these three potential models and their solutions are also obtained. The energy spectrum and potential graphs for each case are discussed for the $\alpha$ deficit angle.