Flat bands in topological media

TL;DR

This paper discusses the emergence of topologically protected flat bands in gapless topological media, which have a high density of states and potential for high-temperature surface superconductivity.

Contribution

It demonstrates that in gapless topological media, the bulk-surface and bulk-vortex correspondence leads to the formation of dispersionless, topologically protected flat bands.

Findings

Flat bands are localized on surfaces with nodal lines and vortex cores with Weyl points.

Flat bands have a highly singular density of states.

Potential for room-temperature surface superconductivity due to flat bands.

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 and in the vortex core in systems with topologically protected Fermi points (Weyl points). 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.