An Interaction Bulk-Boundary Relation and its Applications Towards Symmetry Breaking and Beyond

Our study focuses on interactions between Topological surface matter. Surface fermions in a topological insulator have acquired a lot of attention, particularly for their property that they do not have the Fermion doubling problem, an issue inherent in all fermions in the lattice. Hence if one could engineer an attractive interacting topological surface, the resulting superconducting phase can have emergent Majorana-like elementary excitations. In this respect, we studied the renormalization effect of the gapped bulk fermions on the interacting topological surface matter. We found that the attractive phonon-mediated interaction between the surface fermions is the strongest when the bulk Debye frequency, \Omega_{D} matches the bulk energy gap 'm', a phenomenon we prefer to call 'dynamical resonance'. We also propose a simple scaling relation that connects the interactions between the gapped

bulk topological matter and the gapless surface fermions.