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.