Quasiperiodic criticality and spin-triplet superconductivity in superconductor-antiferromagnet moire patterns

Quasiperiodicity has long been known to be a potential platform to explore exotic phenomena,
realizing an intricate middle point between ordered solids and disordered matter. In particular,
quasiperiodic structures are promising playgrounds to engineer critical wavefunctions, a powerful
starting point to engineer exotic correlated states. Here we show that systems hosting a quasiperodic modulation of antiferromagnetism and spin-singlet superconductivity, as realized by atomic
chains in twisted van der Waals materials, host a localization-delocalization transition as a function
of the coupling strength. Associated with this transition, we demonstrate the emergence of a robust quasiperiodic critical point for arbitrary incommensurate potentials, that appears for generic
relative weights of the spin-singlet superconductivity and antiferromagnetism. We show that inclusion of residual electronic interactions leads to an emergent spin-triplet superconducting state,
that gets dramatically enhanced at the vicinity of the quasiperiodic critical point. Our results put
forward quasiperiodicity as a powerful knob to engineer robust superconducting states, providing
an alternative pathway towards artificially designed unconventional superconductors.