Quantum degenerate Majorana surface zero modes in two-dimensional space

We investigate the topological properties of spin-polarized fermionic polar molecules loaded in a multilayer structure with the electric dipole moment polarized to the normal direction. When polar molecules are paired by attractive interlayer 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 one-dimensional (1D) Kitaev ladders labeled by in-plane momenta k(parallel to) and -k(parallel to), and hence belongs to the BDI class characterized by the winding number Z, protected by the time-reversal symmetry. The Majorana surface modes exhibit a flat band 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. We further show that additional interference fringes can be identified as a signature of such 2D Majorana surface modes in the time-of-flight experiment.