Vortex dynamics simulation in high-T$_{c}$ superconductors with planar pinning arrays coexisting with point pinning sites

The enhancement of critical currents $J_{c }$ by introducing artificial pinning sites is key issue in the application of high-T$_{c}$ superconductors. Planar defects such as twin boundary are well known as the possible candidates for tangible pinning sites. Recently, the improvement of $J_{c }$ has been reported in the samples having high-density planar defects. However, the pinning characteristics of planar defects, especially the change of the pinning efficiency in the presence of point pinning, are still unclear. We have studied the dynamics of vortices interacting with both planar pinning and point pinning sites using molecular dynamics simulation. We have fixed the pinning strength of planar pinning, and calculated the $J_{c}$ as a function of the point pinning strength $f_{p}$. With increasing $f_{p}$, $J_{c}$ changes from $J_{c}\mathbin{\lower.3ex\hbox{$\buildrel{\mathbin{\buildrel\scriptstyle.\hfill\over {\smash{\scriptstyle=}\vphantom{_{\scriptstyle x}}}}}\over {\hfill\smash{\scriptstyle\cdot}}$}} J_{pl}$ ($J_{pl}$: $J_{c}$ obtained in the system without point pinning) to $J_{c}\mathbin{\lower.3ex\hbox{$\buildrel{\mathbin{\buildrel\scriptstyle.\hfill\over {\smash{\scriptstyle=}\vphantom{_{\scriptstyle x}}}}}\over {\hfill\smash{\scriptstyle\cdot}}$}} J_{p}+\alpha $, ($J_{p}$: $J_{c}$ obtained in the system without planar pinning) and then to $J_{c}\mathbin{\lower.3ex\hbox{$\buildrel{\mathbin{\buildrel\scriptstyle.\hfill\over {\smash{\scriptstyle=}\vphantom{_{\scriptstyle x}}}}}\over {\hfill\smash{\scriptstyle\cdot}}$}} J_{p}$. This behavior corresponds to the appearance of the kink structure and the drastic change of $c$-axis correlation function of the vortices. We have also performed the similar calculation with different anisotropy parameters and observed that the stiffness of vortex line changes the $J_{c}$ behavior as a function of $f_{p}$.