Abstract:We investigate the topological properties of spin polarized fermionic polar molecules loaded in a multi-layer structure with the electric dipole moment polarized to the normal direction. When polar molecules are paired by attractive inter-layer interaction, unpaired Majorana fermions can be macroscopically generated in the top and bottom layers in dilute density regime. We show that: the resulting topological state is effectively composed by a bundle of 1D Kitaev ladders labeled by in-plane momenta k and -k, and hence belongs to BDI class characterized by the winding number Z, protected by the time reversal symmetry. The Majorana surface modes exhibit a flatband at zero energy, fully gapped from Bogoliubov excitations in the bulk, and hence becomes an ideal system to investigate the interaction effects on quantum degenerate Majorana fermions.