  We study topological superconductor in one-dimensional (1D) mosaic lattice
whose on-site potentials are modulated for equally spaced sites. When the
system is topologically nontrivial, Majorana zero modes appear at the two ends
of the 1D lattice. By calculating energy spectra and topological invariant of
the system, we find the interval of the mosaic modulation of the on-site
potential, whether it is periodic, quasiperiodic, or randomly distributed, can
influence the topological properties significantly. For even interval of the
mosaic potential, the system will always exist in the topological
superconducting phase for any finite on-site potentials. When the interval is
odd, the system undergoes a topological phase transition and enters into the
trivial phase as the on-site potentials become stronger than a critical value,
except for some special cases in the commensurate lattices. These conclusions
are proven and the phase boundaries determined analytically by exploiting the
method of transfer matrix. They reveal that robust Majorana zero modes can
arise in 1D mosaic lattice independent of the strength of the spatially
modulated potentials.
