  The one-dimensional Su-Schrieffer-Heeger (SSH) model is central to band
topology in condensed matter physics, which allows us to understand and design
distinct topological states. In this work, we find another mechanism to
analogize the SSH model in a spinful system, realizing an obstructed atomic
insulator by introducing intrinsic spin-orbit coupling and in-plane Zeeman
field. In our model, the midgap states originate from a quantized hidden
polarization with invariant index $\mathbb{Z}_2$ (0; 01) due to the local
inversion symmetry breaking. When the global inversion symmetry is broken, a
charge pumping is designed by tuning the polarization. Moreover, by introducing
the $p+ip$ superconductor pairing potential, a new topological phase dubbed
obstructed superconductor (OSC) is identified. This new state is characterized
by invariant index $\mathbb{Z}_2$ (0; 01) and nonchiral midgap states. More
interestingly, these nonchiral edge states result in a chiral-like nonlocal
conductance, which is different from the traditional chiral topological
superconductor. Our findings not only find another strategy to achieve a
spinful SSH model but also predict the existence of OSC, providing a promising
avenue for further exploration of its transport properties.
