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We show that periodic lattice of Abrikosov vortices in chiral $p$ wavesuperconductor in general supports fermionic states with zero energy providedthe intervortex distance is smaller than the critical one. The zero modesappear at the intersection with the Fermi level of electronic magnetic Blochbands formed by the overlapping vortex core states. The Bloch bands are robustagainst lattice disorder induced by fluctuations of vortex positions and cantransmit the energy flow across the lattice. The hallmark of zero modes onBloch bands in electronic heat conductivity is discussed.

Majorana fermions on the Abrikosov flux lattice in a $p_x+ip_y$ superconductor and thermal conductivity in superclean regime