Additionally, although we obtain a sharp resonance condition in a calculation of the spectrum at zero temperature, we note that this resonance will be broadened by finite temperature and a coupling to external leads in a transport experiment; in this case, one should observe a zero-bias conductance peak if the broadening is larger than the energy of the ABS.

The results of our analytical calculation are summarized in Fig. \[analytics\]. In Fig. \[analytics\](a), we show by solving Eq.  numerically that the energy of the subgap ABS oscillates as a function of $k_{so}L$. Furthermore, we show in Fig. \[analytics\](b) that if the system is tuned to the resonance condition $\cos(2k_{so}L)=0$ (assuming $\mu=0$), the ABS becomes pinned near zero energy as a function of Zeeman energy $\Delta_Z$ as predicted in Eq. . As $k_{so}L$ is tuned away from resonance, the ABS becomes less pinned as shown in Figs. \[analytics\](c-d). Thus, within our analytical model we have shown that an ABS can be pinned near zero energy for $\alpha/L\ll\Delta_Z\ll E_{so}$. While these are rather stringent restrictions on the spin-orbit strength, we show in Appendix \[appA\] by numerically diagonalizing the model defined in Eq.  that these inequalities can be loosened to $\alpha/L\lesssim\Delta_Z\lesssim E_{so}$ while 