Dirac Fermions with Electric Dipole Moment and Position-dependent Mass in the Presence of a Magnetic Field Generated by Magnetic Monopoles

Abstract

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. 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 \(m_j\), and explicitly depends on the EDM d, PDM parameter \(\kappa \), magnetic charge density \(\lambda _m\), and on the spinorial parameter s. In particular, the quantization is a direct result of the existence of \(\kappa \) (i.e., \(\kappa \) acts as a kind of “external field or potential”). Besides, we also analyze the nonrelativistic limit of our results, that is, we also obtain the nonrelativistic bound-state solutions. In both cases (relativistic and nonrelativistic), we discuss in detail the characteristics of the spectrum as well as graphically analyze its behavior as a function of \(\kappa \) and \(\lambda _m\) for three different values of n (ground state and the first two excited states).