can vary greatly depending on the precise value of $d$, while the renormalization of material parameters is weakened as $t$ is made smaller. However, as shown in Fig. \[fig3\], we find that varying the thickness $d$ \[Fig. \[fig3\](a)\] and tunneling strength $t$ \[Fig. \[fig3\](b)\] has no appreciable effect on the pinning of the ABS. As changing these parameters drastically alters the topological properties of the system (see Appendix \[appB\] for a more detailed discussion), we can conclude that the presence of a low-energy ABS is determined entirely by the properties of the dot region [@numerics].

In further support of this conclusion, we also calculate the spectrum of the system in the absence of a quantum dot ($L=0$). As shown in Fig. \[nodot\], there are no low-energy states in this case because the topological phase transition occurs for magnetic field strength $B>B_c$. As a result, one essentially observes only the closing of the energy gap in the superconducting layer. Note that there is one subgap ABS, but this state remains very close to the gap edge, consistent with the findings of Refs. [@Aseev:2018; @Huang:2018].

![Changing the thickness of the superconductor $d$ and the strength of the proximity coupling $t$ does not 