Topological insulator realization induced by fermionic interaction through BF mediators

Abstract

This paper demonstrates that ordinary fermions, interacting via a BF mediator, form a renormalized structure with non-trivial topological properties. We explore the analogy between the renormalized fermion and a subset of real three-dimensional topological insulators (TIs) in the vicinity of their single Dirac cones. Using the typical magnitude of TI lattice and gaps, we constrain model parameters. The topological structure induced by radiative corrections enters a class of modified Dirac equations, ensuring the existence of helical gapless near-boundary modes. We derive an effective potential for inter-quasi-particle interactions that incorporates finite-size effects in the axial direction, revealing signatures of spin-orbit coupling and time-reversal invariance. Remarkably, particles with different spins do not interact via the characteristic spin-orbit coupling, and a non-central spin-dependent force arises. We also address the behavior of the system in the phase transition associated with the thin-film limit.