Flat bands in topological media

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Abstract
Topological media are systems whose properties are protected by topology and thus are robust to deformations of the system. In topological insulators and superconductors the bulk-surface and bulk-vortex correspondence gives rise to the gapless Dirac or Majorana fermions on the surface of the system and/or inside the vortex core. In gapless topological media, the bulk-surface and bulk-vortex correspondence is more effective: it produces topologically protected gapless fermions without dispersion - the flat band. Fermion zero modes forming the flat band are localized on the surface of the three-dimensional topological media with protected nodal lines and in the vortex core in the systems with topologically protected Dirac points. Flat band has an extremely singular density of states, which may give rise in particular to surface superconductivity with an unusually high transition temperature.

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