  Topological superconductors (TSCs) are correlated quantum states with
simultaneous off-diagonal long-range order and nontrivial topological
invariants. They produce gapless or zero energy boundary excitations, including
Majorana zero modes and chiral Majorana edge states with topologically
protected phase coherence essential for fault-tolerant quantum computing.
Candidate TSCs are very rare in nature. Here, we propose a novel route toward
emergent quasi-one-dimensional (1D) TSCs in naturally embedded quantum
structures such as atomic line defects in unconventional spin-singlet $s$-wave
and $d$-wave superconductors. We show that inversion symmetry breaking and
charge transfer due to the missing atoms lead to the occupation of incipient
impurity bands and mixed parity spin singlet and triplet Cooper pairing of
neighboring electrons traversing the line defect. Nontrivial topological
invariants arise and occupy a large part of the parameter space, including the
time reversal symmetry breaking Zeeman coupling due to applied magnetic field
or defect-induced magnetism, creating TSCs in different topological classes
with robust Majorana zero modes at both ends of the line defect. Beyond
providing a novel mechanism for the recent discovery of zero-energy bound
states at both ends of an atomic line defect in monolayer Fe(Te,Se)
superconductors, the findings pave the way for new material realizations of the
simplest and most robust 1D TSCs using embedded quantum structures in
unconventional superconductors with large pairing energy gaps and high
transition temperatures.
