Magnetic flux-driven modulation of Weyl pair dynamics on catenoid bridge: A theoretical analysis

Abstract

In this study, we examine the behavior of a Weyl pair influenced by magnetic flux on a catenoid bridge by obtaining analytical solutions of the corresponding fully covariant two-body Dirac equation. By deriving a non-perturbative wave equation governing their relative motion, we obtain a solution expressed in terms of the Confluent Heun function. Our findings indicate that the dynamics of this pair are influenced not only by the magnetic flux but also by the radius (ρ) of the catenoid bridge. We observe that the ground state energy of the Weyl pair can vary significantly, shifting from 0.258eV to 1.8 meV as the ρ value changes from 10nm to 1 μm. Furthermore, our results show that the Weyl pair’s behavior can resemble that of either a single fermion or boson, and intriguingly, this behavior can be modulated by adjusting the magnetic flux.