pairing potential of the superconducting layer, whereas the $\Delta$ appearing in Sec. \[analytical\] represented the proximity-induced superconducting gap in the bulk of the nanowire. The nanowire and superconductor are coupled via local spin-conserving tunneling of the form $$H_t=-t\sum_{x=L+1}^{L+L_s-1}\{c^\dagger_{x,1}b_x+H.c.\},$$ where $t$ is the hopping amplitude between the nanowire and superconductor, which parametrizes the strength of the proximity coupling.

![\[wf\] Probability density $|\psi_{x,y}|^2$ of the low-energy ABS (a) within the nanowire ($y=1$) and (b) within the superconductor (with a line cut taken along $x=350$). Because $d$ is much smaller than the superconducting coherence length, the wave function does not decay in the $y$-direction. The total weight of the wave function within the quantum dot is 0.32, the total weight in the proximitized nanowire region is 0.11, and the total weight in the superconductor is 0.57. Parameters are the same as in Fig. \[fig2\](b), with $\Delta_Z/\Delta_0=5$.](wf.pdf){width="\linewidth"}

To determine how to tune the system to observe an ABS pinned to zero energy, we first fix the magnetic field strength relatively close to the critical field of the superconductor and calculate the energy of the lowest subgap ABS as a function of spin-orbit strength $\alpha$. As the pinning behavior is optimized for $\mu=0$, we assume 