Kerr effect in (1 + 2)-dimensional graphene wormhole with axial magnetic field

Abstract

We investigate the effects of the magnetic field, relaxation time, wormhole radius, and curvature radius on the Kerr effect in a (1 + 2)-dimensional graphene wormhole. By applying an external magnetic field along the wormhole's axis, we formulate and analytically solve the Dirac equation under constant magnetic flux. For the scenario of a constant magnetic field, we derive the quantized energy levels and corresponding eigenstates. The numerical results show that the orbital angular momentum (OAM), radius of curvature and wormhole coordinate can effectively control the linear Kerr effect by modifying electronic states, affecting interference patterns, altering the electronic band structure, introducing effective gauge fields, increasing interaction volumes and tuning potential landscapes. These mechanisms collectively allow for a tunable and responsive Kerr effect in the material.