that the chemical potential is tuned in such a way. Consistent with the analytical model of Sec. \[analytical\] and as shown in Fig. \[fig2\](a), the energy of the subgap ABS depends on $\alpha$ in an oscillatory way, with the energy passing through zero only for specific values of $\alpha$. After fixing $\alpha$ such that the ABS energy is small (i.e., after fine-tuning the system so there is a low-energy state), we then calculate the full ABS spectrum as a function of field strength. As shown in Fig. \[fig2\](b), we find for this specific value of $\alpha$ that the ABS is pinned near zero energy for a large range of field strength [@spinx]. Note that no topological phase transition occurs in Fig. \[fig2\](b), as this requires a field strength that exceeds the critical field of the superconductor, $B>B_c$ (we also show this explicitly in Appendix \[appB\]). For the chosen parameters (which are given in the caption of Fig. \[fig2\]), we find that the ABS becomes pinned near zero energy at a Zeeman energy of about $\Delta_Z\approx4\Delta_0$ and remains pinned all the way up to $\Delta_Z^c$. This is also consistent with the analytical results of Sec. \[analytical\], where it was shown that 