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

Abstract: We show that periodic lattice of Abrikosov vortices in chiral $p$ wave superconductor in general supports fermionic states with zero energy provided the intervortex distance is smaller than the critical one. The zero modes appear at the intersection with the Fermi level of electronic magnetic Bloch bands formed by the overlapping vortex core states. The Bloch bands are robust against lattice disorder induced by fluctuations of vortex positions and can transmit the energy flow across the lattice. The hallmark of zero modes on Bloch bands in electronic heat conductivity is discussed.