  The Su-Schrieffer-Heeger (SSH) model describes a finite one-dimensional dimer
lattice with first-neighbour hoppings populated by non-interacting electrons.
In this work we study a generalization of the SSH model including longer-range
hoppings, what we call the extended SSH model. We show that the presence of odd
and even hoppings has a very different effect on the topology of the chain. On
one hand, even hoppings break particle-hole and sublattice symmetry, making the
system topologically trivial, but the Zak phase is still quantized due to the
presence of inversion symmetry. On the other hand, odd hoppings allow for
phases with a larger topological invariant. This implies that the system
supports more edge states in the band's gap. We propose how to engineer those
topological phases with a high-frequency driving. Finally, we include a
numerical analysis on the effect of diagonal and off-diagonal disorder in the
edge states properties.
