  We analyze influence of a dimerization on the topological phases of the
Rashba nanowire proximitized to a superconducting substrate. We find that
periodic alternations of the hopping integral and spin-orbit coupling can lead
to band inversion, inducing transition to topologically nontrivial
superconducting phase that hosts the Majorana zero-energy modes. This
"dimerization-induced topological superconductivity" completely repels the
topological phase of the uniform nanowire, whenever they happen to overlap. We
provide an analytical justification for this puzzling behavior based on the
symmetry/parity considerations and discuss feasible spectroscopic methods for
its empirical observation. We also test stability of the topological
superconducting phases against electrostatic disorder.
