Dirac fermions with electric dipole moment and position-dependent mass in the presence of a magnetic field generated by magnetic monopoles

In this paper, we determine the bound-state solutions for Dirac fermions with electric dipole moment (EDM) and position-dependent mass (PDM) in the presence of a radial magnetic field generated by magnetic monopoles. To achieve this, we work with the (2+1)-dimensional (DE) Dirac equation with nonminimal coupling in polar coordinates. Posteriorly, we obtain a second-order differential equation via quadratic DE (simplified by a similarity transformation). Solving this differential equation through a change of variable and the asymptotic behavior, we obtain a generalized Laguerre equation. From this, we obtain the bound-state solutions of the system, given by the two-component Dirac spinor and by the relativistic energy spectrum. So, we note that such spinor is written in terms of the generalized Laguerre polynomials, and such spectrum (for a fermion and an antifermion) is quantized in terms of the radial and total magnetic quantum numbers n and mⱼ, and explicitly depends on the EDM d, PDM parameter κ, magnetic charge density λₘ, and on the spinorial parameter s. In particular, the quantization is a direct result of the existence of κ (i.e., κ acts as a kind of ``external field or potential''). Besides, we discuss in detail the characteristics of the spectrum as well as graphically analyze the behavior of the spectrum as a function of κ and λₘ for three different values of n (ground state and the first two excited states).