Topological materials with extensive flat-band surface states

Abstract: Materials that have zero-energy flat band states on the surface are likely to show surface superconductivity. Here we report a theoretical observation that a Hamiltonian describing a thin slab of topological nodal line semimetal, has zero energy eigenstate spanning the entire surface under certain conditions, namely (i) the hopping probability of fermions in the direction of thickness is more than that in other directions (ii) the onsite interaction should be less than some limiting value determined by the hopping probability. Our claim is substantiated by analytic and numerical approach. We also report new phase transitions in a region of parameter space and indicate that the Hamiltonian can also be realised by stacked layers described by Kitaev model on honeycomb lattice.