Strain Effects on the Electronic Properties of a Graphene Wormhole

In this work, we explore the strain and curvature effects on the electronic properties of a curved graphene structure, called the graphene wormhole. The electron dynamics is described by a massless Dirac fermion containing position-dependent Fermi velocity. In addition, the strain produces a pseudo-magnetic vector potential to the geometric coupling. For an isotropic strain tensor, the decoupled components of the spinor field exhibit a supersymmetric (SUSY) potential, depending on the centrifugal term and the external magnetic field only. In the absence of an external magnetic field, the strain yields an exponentially damped amplitude, whereas the curvature leads to a power-law damping of the wave function. The spin-curvature coupling breaks the chiral symmetry between the upper and the lower spinor component, which leads to the increasing of the wave function on either upper or lower region of the wormhole, i.e., depending on the spin number. By adding a uniform magnetic field, the effective potential exhibits an asymptotic quadratic profile and a spin-curvature barrier near the throat. As a result, the bound states (Landau levels) are confined around the wormhole throat showing an asymmetric and spin-dependent profile.