EUROPEAN PHYSICAL JOURNAL PLUS, vol.139, pp.1-7, 2024 (SCI-Expanded)
In this manuscript, we investigate the interaction between a fermion–antifermion pair in (2 + 1)-dimensions, governed by
a Coulomb-type inter-particle potential. We explore analytical solutions for a fully covariant two-body Dirac equation derived from
quantum electrodynamics, focusing on a spinless composite system. We present a non-perturbative second-order wave equation and
derive a solution using the generators of the s2 algebra. Subsequently, we determine the relativistic frequency modes of the system
and extend our findings to electron–hole pairs in a monolayer medium in the vicinity of substrate. We analyze the impact of the
effective dielectric constant (ε) of the surrounding medium on the real and damped modes of an exciton. Our results indicate that
the ground state binding energy of the system can vary from the order of eV to a few meV, depending on changes in ε. Additionally,
we observe that the decay time for the ground state of such an exciton is on the order of ∼ 10−12 s. These findings suggest that the
evolution of such a pair can be controlled by adjusting the effective dielectric constant of the surrounding medium.