  Zeeman fields can drive semiconductor quantum wires with strong spin-orbit
coupling and in proximity to s-wave superconductors into a topological phase
which supports end Majorana fermions and offers an attractive platform for
realizing topological quantum information processing. Here, we investigate how
potential disorder affects the topological phase by a combination of analytical
and numerical approaches. Most prominently, we find that the robustness of the
topological phase against disorder depends sensitively and non-monotonously on
the Zeeman field applied to the wire.
