Planar Josephson junction devices with narrow superconducting strips: Topological properties and optimization

We study the low-energy physics of planar Josephson junction structures realized in a quasi-two dimensional semiconductor system proximity-coupled to narrow superconducting films. Using both a recursive Green's function approach and an effective Hamiltonian approximation, we investigate the topological superconducting phase predicted to emerge in this type of system. We first characterize the effects associated with varying the electrostatic potentials applied within the unproximitized semiconductor regions. We then address the problem of optimizing the width of the superconductor films and identifying the optimal regimes characterized by large topological gap values. We find that structures with narrow superconducting films of widths ranging between about $100~$nm and $200~$nm can support topological superconducting phases with gaps up to $40\%$ of the parent superconducting gap, significantly larger than those characterizing the corresponding wide-superconductor structures. This work represents the first component of a proposed comprehensive strategy to address this optimization problem in planar Josephson junction structures and realize robust topological devices.