  We study the formation of Majorana states in superconductors using the
Majorana polarization, which can locally evaluate the Majorana character of a
given state. We introduce the definition of the Majorana polarization vector
and the corresponding criterion to identify a Majorana state, and we apply it
to some simple cases such as a one-dimensional wire with spin-orbit coupling,
subject to a Zeeman magnetic field, and proximitized by a superconductor, as
well as to an NS junction made with such a wire. We also apply this criterion
to two-dimensional finite-size strips and squares subject to the same physical
conditions. Our analysis demonstrates the necessity of using the Majorana
polarization local order parameter to characterize the Majorana states,
particularly in finite-size systems.
