for generating a low-energy ABS in such a system, we consider a minimal model in which the proximitized region of the nanowire has no SOI. While we focus on the case where a nanowire with intrinsic SOI is strongly coupled to a superconductor (thereby renormalizing the SOI via the proximity effect), we emphasize that such a model can apply to more general cases as well; e.g., the minimal model can also describe a nanowire with no intrinsic SOI that is weakly coupled to a superconductor, with local gates generating SOI only in the quantum dot region. Through an analytical solution of the ABS spectrum in this model, we find that a low-energy ABS is present if the chemical potential is tuned within the Zeeman gap and if the length of the nanowire region that is left uncovered by the superconductor (the quantum dot) is finely tuned with respect to the spin-orbit length to fulfill a resonance condition. Importantly, the presence of the ABS is sensitive only to properties of the dot and is therefore unrelated to topological superconductivity.

It was found in Refs. [@Reeg:2017_3; @Reeg:2018] that a strong proximity coupling causes a significant renormalization of semiconducting material parameters and generally 