  Majorana zero modes in a superconductor-semiconductor nanowire have been
extensively studied during the past decade. Disorder remains a serious problem,
preventing the definitive observation of topological Majorana bound states.
Thus, it is worthwhile to revisit the simple model, the Kitaev chain, and study
the effects of weak and strong disorder on the Kitaev chain. By comparing the
role of disorder in a Kitaev chain with that in a nanowire, we find that
disorder affects both systems but in a nonuniversal manner. In general,
disorder has a much stronger effect on the nanowire than the Kitaev chain,
particularly for weak to intermediate disorder. For strong disorder, both the
Kitaev chain and nanowire manifest random featureless behavior due to universal
Anderson localization. Only the vanishing and strong disorder regimes are thus
universal, manifesting respectively topological superconductivity and Anderson
localization, but the experimentally relevant intermediate disorder regime is
nonuniversal with the details dependent on the disorder realization in the
system.
