  Higher-order topological crystalline phases in low-dimensional interacting
quantum systems represent a challenging and largely unexplored research topic.
Here, we derive a Hamiltonian describing fermions interacting through
correlated hopping processes that break chiral invariance, but preserve both
inversion and time-reversal symmetries. In this way, we show that our
one-dimensional model gives rise to an interacting second-order topological
insulating phase that supports gapped edge states. The topological nature of
such interacting phase turns out to be revealed by both long-range order of a
non-local string correlation function and by even degeneracy of the
entanglement spectrum. For strong interactions we instead find that the
topological crystalline phase is destroyed and replaced by a singlet
superconducting phase. The latter, characterized by local fermionic pairing,
turns out to appear both in a homogeneous and in a phase separated form.
Relevantly, the derived one-dimensional model and the second-order topological
insulator can be explored and investigated in atomic quantum simulators.
