  A chiral symmetric Su-Schrieffer-Heeger (SSH) chain features topological end
states in one of its dimerized configurations. Those mid-gap zero energy states
show interesting modifications upon a periodic tuning of the hopping
modulations. Besides, more and more in-gap end modes appear at nonzero energies
for further partitioning of the Brillouin zone (BZ) due to increased hopping
periodicity. The new topological phases are identified with a detailed analysis
of the topological invariants namely, winding number and Zak phases. The
spectra and topology of these systems with periodically modulated hopping are
studied also in the presence of a single static domain wall, separating two
topologically inequivalent dimerized structures. The domain wall causes
additional in-gap modes in the spectrum as well as zero energy domain wall
solitonic states for specific hopping periodicities. We also study the effect
of disorder, particularly the chirality breaking onsite ones, on the edge and
domain wall states. Other than the SSH type we also consider random, Rice-Mele
or AI type disorder to do a comparative analysis of the evolution of chirality
and zero energy states as the strength of disorder and hopping periodicity is
varied. Our findings can add important feedback in utilizing topological phases
in various fields including quantum computations while the results can be
easily verified in a cold atom set up within optical lattices.
