Realistic models for Majorana wires

We construct realistic effective models to theoretically facilitate the experimental search for Majorana modes in quantum wires. Starting with an accurate first-principles calculation, we provide a detailed discussion of finite size and multiband effects, and of the spin-orbit splitting. We also present a thorough consideration of proximity induced superconductivity, extensively supporting it with numerical evidence. The comparison of our results to previously used models and actual experiments is done.