  Majorana zero modes in the superconductor-semiconductor nanowire have been
extensively studied during the past decade. Disorder remains a serious problem
preventing the definitive observation of the topological Majorana bound states.
Thus, it is worthwhile to revisit the simple model -- Kitaev chain, and study
the effects of weak and strong disorder on the Kitaev chain. By comparing the
role of disorder in the Kitaev chain with that in the 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
Kitaev chain and nanowire manifest random featureless behavior due to the
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 non-universal with the details dependent on the disorder realization
in the system.
