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

TL;DR

This paper derives bound-state solutions for Dirac fermions with electric dipole moments and position-dependent mass in a radial magnetic field from magnetic monopoles, revealing how quantum numbers and parameters influence the spectrum.

Contribution

It presents a novel analytical solution for Dirac fermions with EDM and PDM in a magnetic monopole field, including relativistic and nonrelativistic spectra, highlighting the role of PDM parameter as an external potential.

Findings

Bound-state solutions expressed via generalized Laguerre polynomials.

Quantized energy spectrum depending on quantum numbers and physical parameters.

Spectrum characteristics analyzed for different quantum states and parameters.

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).