Critical thickness of the thickness-driven topological transition

Determine the exact critical thickness at which the BF-mediated fermionic system undergoes the transition from a topological phase to a trivial thin-film phase.

Background

The paper argues that reducing the slab thickness enhances inter-boundary coupling and can destroy the topological character of the renormalized fermionic structure. This qualitative mechanism is compared with thickness-driven transitions observed in materials such as HgTe, Bi2_2Te3_3, and Bi2_2Se3_3.

Because the calculation uses an effective long-distance continuum description rather than a microscopic lattice model, the authors state that it cannot fix the material-specific threshold thickness. Determining that critical thickness requires microscopic parameters beyond the framework developed in the paper, including the relevant cutoff, effective Fermi velocities, and surface-state penetration behavior.

References

However, since the analysis is based on an effective long-distance description, it cannot determine the exact critical thickness associated with the phase transition.

— Topological insulator realization induced by fermionic interaction through BF mediators  (2608.16660 - Gracia et al., 17 Aug 2026) in Section 4, subsection “On the thin-film limit”