Reentrant topological phases and spin density wave induced by 1D moir\'e potentials

Recent studies of 2D moir\'e materials have opened opportunities for advancing condensed matter physics. However, the effect of 1D moir\'e potentials on topological and correlated phases remains largely unexplored. Here we reveal a sequence of trivial-to-topological transitions and periodic-moir\'e-spin density waves induced by the 1D commensurate moir\'e potentials for spin-1/2 fermionic atoms. Such reentrant topology from a trivial phase is absent without the moir\'e potential and can be understood as the renormalization of topological parameters by the moir\'e strength. We then unveil the critical exponent and localization properties of the single-particle eigenstates. The periodic spin density wave of many-body ground states is contributed by the moir\'e potential, and is enhanced by on-site interactions but suppressed by nearest-neighbor interactions. Our results enrich the topological physics with multiple transitions and spin-density orders in 1D moir\'e systems, and the realization of the proposed model is promising in near-future ultracold atom setups.