Flat band in the core of topological defects: bulk-vortex correspondence in topological superfluids with Fermi points

TL;DR

This paper explores the emergence of flat bands at zero energy within vortices in topological superfluids with Fermi points, revealing a bulk-vortex correspondence analogous to bulk-surface relations in topological materials.

Contribution

It introduces the concept of flat bands in vortex cores linked to bulk Fermi points, extending topological correspondence principles to vortex defects in superfluids.

Findings

Flat bands are localized in vortex cores with zero energy.

The flat band boundaries are determined by projections of bulk Fermi points.

The bulk-vortex correspondence parallels bulk-surface topological relations.

Abstract

We discuss the dispersionless spectrum with zero energy in the linear topological defects - vortices. The flat band emerges inside the vortex living in the bulk medium containing topologically stable Fermi points in momentum space. The boundaries of the flat band in the vortex are determined by projections of the Fermi points in bulk to the vortex axis. This bulk-vortex correspondence for flat band is similar to the bulk-surface correspondence discussed earlier in the media with topologically protected lines of zeroes. In the latter case the flat band emerges on the surface of the system, and its boundary is determined by projection of the bulk nodal line on the surface.