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∼Δ √{R } exceeds the mean level spacing for the chiral branch ω₀∼Δ²/E_F , already for very small values of the reflection coefficient off the defect R ≪1 (Δ is the bulk gap). For R ≳√{Δ /E_F } , formation of the minigap is accompanied by the appearance of subgap states localized along the defect, in accordance with A. V. Samokhvalov et al., Phys. Rev. B 102, 174501 (2020), 10.1103/PhysRevB.102.174501. 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 ∼(Δ /ω₀) √{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 π .