Kitaev chains realized in quantum dots coupled via superconducting segments provide a controllable platform for engineering Majorana zero modes (MZMs). In these systems, subgap states in the hybrid region mediate the effective coupling between quantum dots and determine the emergence of sweet spots where MZMs are strongly localized. However, existing minimal treatments often oversimplify the mesoscopic hybrid region. We perform a full microscopic treatment of this hybrid segment, capturing the quasiparticle continuum and spin-split Andreev bound states (ABSs), and show that it fundamentally alters the minimal picture. We derive analytical expressions for the renormalized couplings and sweet-spot conditions, establishing a direct link between microscopic chain parameters and Majorana optimization and identifying experimentally relevant regimes for improved device performance. Critically, we find that parity crossings of the ABS, marking the onset of an odd-parity spin-polarized regime in the segment, identify the optimal operating windows where MZMs are simultaneously well localized with a large gap to excited states.

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• Majorana zero modes
• Mesoscopics
• Superconductivity
• Quantum dot qubits
• Superconducting qubits
• Green's function methods
• Kitaev model
• Tight-binding model