  Finite-length one-dimensional topological superconductor wires host localized
Majorana zero modes at their ends. In realistic models, these appear only after
a topological quantum critical point is crossed by external tuning of
parameters. Thus, there is a universal finite-size scaling, governed by the
critical point, that dictates the evolution of the energy of the Majorana modes
near the transition. We first describe this scaling, then apply it in detail to
an explicit synthetic topological superconductor model. Our work not only
connects Ising quantum criticality with realistic nanowires in the presence of
spin-orbit coupling, Zeeman splitting and superconductivity, but also provides
a viable experimental route for discerning the existence of the topological
quantum critical point.
