Flat Midgap Topological Surface and Hypersurface Bands without Parameter Tuning

The Su-Schrieffer-Heeger model is extended to the three and higher dimensional systems. Nearly or absolutely flat midgap surface and hypersurface bands are predicted based on the topological analysis, which do not require fine tuning of parameters. By adding the on-site Coulomb interaction for the three dimensional systems, we computationally show that the large difference in the band widths between the surface and the bulk leads to the strongly correlated phenomena, specifically magnetism, confined only on the surface. Possible experimental realizations in solid state materials and metamaterials are discussed.