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Using the spatial dependence of the penetration depth derived from the electron scattering mechanism near a planar defect (twin or grain boundary), the London formalism has been revisited. We used a perturbative approach to calculate the magnetic field of a vortex in the presence of a planar defect. Moreover, the vortex energy has been derived as a function of the vortex-defect distance. We found the interaction between the vortex and the defect to be attractive. However, the vortex core is not pinned on the plane but at a distance of 90 Å at zero temperature. As the temperature increases, the vortex pinning energy and the vortex-plane defect distance decrease. Due to the thermal fluctuation a transition is occurring such that for T < T tr the vortex is oscillating around one well position, as for T < T tr the vortex is oscillating in the self-consistent well formed by the two wells which are symmetric with respect to the plane defect, and so the vortex appears to be vibrating around the plane defect.

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