Magnetic field of a single vortex in the presence of a planar defect: vortex pinning by a planar defect

Abstract

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.

Microscopic model of a planar defect in a superconductor

“…Let us apply our results to the pinning of a single vortex by a planar defect. In a previous work [6], using the phenomenological spatial dependence for the penetration depth derived from electron scattering near a planar defect, the London formalism has been revisited with the perturbation approach to calculate the magnetic field of a vortex in the presence of a planar defect and therefore to investigate the pinning. Let us give only a flavour of the calculation and finally apply it to examine the influence of the calculated spatial dependence of the penetration depth on the vortex pinning by a planar defect.…”

“…The vortex energy is obtained by adding the core energy to the screening energy. A more detailed account of the method is reported in [6].…”

“…Figure 5. Vortex energy in units of (φ 0 /2πλ 0 ) 2 /2µ 0 as a function of the vortex position x v , in units of λ 0 , at T = 10 and 50 K for a defect strength η = 10 −4 .has shown that the vortex could be pinned in two possible symmetric positions[6] (x = 29 or −29 Å). The effect of the thermal fluctuations is vibration in the wells and if the vibration amplitudes are significantly large the vortex could jump from one well to another.…”