a regime in which there is a low-energy ABS and demonstrate that this ABS is sensitive only to properties of the quantum dot. Finally, we show that if the quantum dot is removed from the system so no low-energy ABSs can form, no zero-energy states are present because the strong proximity coupling drives the topological phase transition to field strengths exceeding the critical field of the superconducting layer.

![(a) We first fix $\Delta_Z=0.75\Delta_Z^c$ and find that the energy $E$ of the lowest subgap ABS oscillates as a function of spin-orbit strength $\alpha$. The solid blue curve corresponds to $\mu=0$ while the dashed green curve corresponds to $\mu=-3\Delta_0$. The resonance condition, which is determined by points at which the energy of the ABS pass through zero, is altered by changes in $\mu$. (b) For $\mu=0$, we tune to the resonant value $\alpha/t_{sc}=0.538$ \[as indicated in panel (a)\] and find an ABS (red) that is pinned near zero energy over a large range of Zeeman energy $\Delta_Z$. Higher energy states are shown in black. (c) For $\mu=-3\Delta_0$, we tune to a different resonant value $\alpha/t_{sc}=0.575$ and again find a pinned ABS. (d) Tuning away from the resonant value of $\alpha$, we find 