Mitigating disorder-induced zero-energy states in weakly coupled superconductor-semiconductor hybrid systems

Disorder has appeared as one of the main mechanisms to induce topologically trivial zero-energy states in superconductor-semiconductor systems, thereby challenging the detection of topological superconductivity and Majorana bound states. Here, we demonstrate that, for disorder in any part of the system, the formation of disorder-induced trivial zero-energy states can, to a large extent, be mitigated by keeping the coupling between the semiconductor and superconductor weak. The only exception is strong disorder in the semiconductor, where instead the strong-coupling regime is somewhat more robust against disorder. Furthermore, we find that the topo-logical phase in this weak-coupling regime is robust against disorder, with a large and well-defined topological gap which is highly beneficial for topological protection. Our work shows the advantages and disadvantages of weak and strong couplings under disorder, important for designing superconductor-semiconductor hybrid structures.