Vortex core near planar defects in a clean layered superconductor

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