Exact-theory persistence of thin-film spin-orbit cancellation

Determine whether the cancellation of the spin-orbit contribution at planar separation $|\vec r_{\parallel}|=L$ survives in the exact theory beyond the effective long-distance approximation used for the thin-film propagator and interaction potential.

Background

The paper studies boundary-mode interactions mediated by BF fields in a finite-width topological-insulator-inspired system. In the thin-film limit, the authors use a long-distance expansion of the hyperbolic cotangent appearing in the finite-size propagator and find that, for quasi-particle pairs on opposite boundaries with planar separation $|\vec r_{\parallel}|=L$, the characteristic spin-orbit interaction is canceled.

The authors explicitly caution that this result may be an artifact of the approximation. Establishing whether the cancellation remains present when the exact finite-size theory is used would determine whether it represents a genuine physical feature or only a limitation of the effective calculation.