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

• URL: http://arxiv.org/abs/2405.16300v1
• Date: Sat, 25 May 2024 16:49:01 GMT
• Title: Dirac fermions with electric dipole moment and position-dependent mass in the presence of a magnetic field generated by magnetic monopoles
• Authors: R. R. S. Oliveira,
• Abstract summary: We determine the bound-state solutions for Dirac fermions with electric dipole moment (EDM) and position-dependent mass (PDM) In particular, we discuss in detail the characteristics of the spectrum as well as analyze the behavior of the spectrum.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 (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 $m_j$, 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 discuss in detail the characteristics of the spectrum as well as graphically analyze the behavior of the spectrum as a function of $\kappa$ and $\lambda_m$ for three different values of $n$ (ground state and the first two excited states).

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