Vortex core near planar defects in a clean layered superconductor

We investigate the structure of quasiparticle states localized in a core of\nan Abrikosov vortex in a clean layered superconductor in the presence of planar\ndefects. It is shown that even a highly transparent defect opens a minigap at\nthe Fermi energy. Its magnitude, $E_g\\sim\\Delta\\sqrt{R}$, exceeds the mean\nlevel spacing for the chiral branch, $\\omega_0\\sim\\Delta^2/E_F$, already for\nvery small values of the reflection coefficient off the defect, $R\\ll1$\n($\\Delta$ is the bulk gap). For $R\\gtrsim\\sqrt{\\Delta/E_F}$, formation of the\nminigap is accompanied by the appearance of subgap states localized along the\ndefect, in accordance with [A. V. Samokhvalov \\emph{et al.}, Phys.\\ Rev.\\ B\n\\textbf{102}, 174501 (2020)]. The minigap takes its maximal value for the\nvortex located right at the defect, decreases with increasing the distance $b$\nfrom the defect, and closes when $k_Fb\\sim (\\Delta/\\omega_0)\\sqrt{R}$. We also\nstudy various configurations of several planar defects (few crossing planes,\nstars, periodic structures). Although the minigap remains, a strong\ncommensurability effect is observed. For two crossing planar defects, the\nmagnitude of the minigap strongly depends on how close the intersection angle\nis to a rational fraction of $\\pi$.\n