Interaction bulk-boundary relation and its applications towards symmetry breaking and beyond

In this article, we propose a simple but general scaling relation between interactions in a gapped bulk topological matter and gapless interacting surface states. We explicitly illustrate such a generic bulk-boundary relation (BBR) for a few specific interactions in a topological quantum matter, where we can perform dimensional reduction of a microscopic bulk theory to project out interacting surfaces. We have examined renormalization effects of the gapped bulk fermions on the interacting topological surface fermions. As simple applications, we utilize effective interacting quantum fields implied by BBR to explore feasibility of routes to various fascinating emergent phenomena on surfaces including emergent Majorana fermions induced by spontaneous symmetry breaking. We obtain sufficient conditions for these interacting surface phenomena to take place. We have also found that for given bulk electron-phonon interactions and when OD m, the phonon-mediated interactions on the surface are strongest if the bulk Debye frequency S2D matches m, the mass gap of the topological matter.

Automated summary

In this article, we propose a scaling relation between interactions in a gapped bulk topological matter and gapless interacting surface states. We examine the renormalization effects of gapped bulk fermions on interacting topological surface fermions, and explore various emergent phenomena on surfaces using effective interacting quantum fields implied by this relation. We find that phonon-mediated interactions on the surface are strongest when the bulk Debye frequency matches the mass gap of the topological matter.