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VOLUME 94 | ISSUE 3 | PAGE 252
Flat bands in topological media
T. T. Heikkilä*, N. B. Kopnin*+, G. E. Volovik*+
*Low Temperature Laboratory, Aalto University, School of Science and Technology, P.O. Box 15100, FI-00076 AALTO, Finland
+Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia

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 Weyl, Dirac or Majorana fermions on the surface of the system and inside vortex cores. Here we show that 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 topological media with protected nodal lines [Schnyder, Ryu, 2010,Heikkila, Volovik, 2010b] and in the vortex core in systems with topologically protected Fermi points (Weyl points) [Volovik, 2010]. Flat band has an extremely singular density of states, and we show that this property may give rise in particular to surface superconductivity which could exist even at room temperature.


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