Bound states of (2+1)−dimensional massive Dirac fermions in a Lorentzian-shaped inhomogeneous perpendicular magnetic field

• Published in: Physica. E, Low-dimensional systems & nanostructures Vol. 116; p. 113777
• Main Authors: Le, Dai-Nam, Luu, Phong-Su, Ha, Thanh-Sang, Phan, Ngoc-Hung, Le, Van-Hoang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2020
• ISSN: 1386-9477; 1873-1759
• DOI: 10.1016/j.physe.2019.113777

In this paper, we investigate massive Dirac fermions in (2+1)−spacetime confined by a Lorentzian-shaped inhomogeneous magnetic field and construct solutions of their bound states by both analytical and numerical methods. First, we have found a set of specific magnetic fields which allow obtaining conditionally exact solutions as well as quasi-exact ones. Second, we construct these analytical solutions explicitly and analyse the effect of Dirac fermion’s effective mass. We also calculate entire energy spectra for the considered system numerically using Feranchuk–Komarov operator method and combine them with the analytical solutions for investigating Landau quantization in the energy spectrum. •Dirac–Weyl equation on silicene, germanene, and tinene.•Solution of massive Dirac–Weyl equation under Lorentzian-shaped magnetic field.•Effect of tunable mass in considered problems.•Existence of Landau quantization in inhomogeneous magnetic field.