  Su-Schrieffer-Heeger (SSH) model is one of the simplest models to show
topological end/edge states and the existence of Majorana fermions. Here we
consider a SSH like model both in one and two dimensions where a nearest
neighbor hopping features spatially periodic modulations. In the 1D chain, we
witness appearance of new in-gap end states apart from a pair of Majorana zero
modes (MZM) when the hopping periodicity go beyond two lattice spacings. The
pair of MZMs, that appear in the topological regime, characterise the end modes
each existing in either end of the chain. These, however, crossover to both-end
end modes for small hopping modulation strength in a finite chain. Contrarily
in a 2D SSH model with symmetric hopping that we consider, both non-zero and
zero energy topological states appear in a finite square lattice even with a
simple staggered hopping, though the zero energy modes disappear in a ribbon
configuration. Apart from edge modes, the 2D system also features corner modes
as well as modes with satellite peaks distributed non-randomly within the
lattice. In both the dimensions, an increase in the periodicity of hopping
modulation causes the zero energy Majorana modes to become available for either
sign of the modulation. But interestingly with different periodicity for
hopping modulations in the two directions, the zero energy modes in a 2D model
become rarer and does not appear for all strength and sign of the modulation.
