Topological materials with extensive flat-band surface states

Materials that have zero-energy flat band states on the surface may 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 of the Brillouin zone under certain conditions, namely (i) the hopping amplitude of fermions in the direction of thickness is more than that in other directions (ii) the onsite energy 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 a suitable Hamiltonian.