What happens when a moire-like commensurate modulation is imposed on the Zeeman field of a one-dimensional chiral (class AIII) topological insulator of ultracold fermions. Two effects follow. First, increasing the moire strength does not simply destroy the topology: the winding number switches repeatedly, producing a reentrant trivial-topological-trivial-topological-trivial sequence whose windows survive weak on-site disorder, with boundaries located by finite-size scaling of the localization length and by the fidelity susceptibility. Second, even an infinitesimal moire potential nucleates a periodic-moire spin density wave commensurate with the beat supercell; on-site Hubbard repulsion U enhances it while nearest-neighbour repulsion V suppresses it and eventually replaces it with a period-two charge density wave. The many-body Berry phase shows part of the spin-density-wave region is itself topological. Both effects are explained by a single mechanism: the moire modulation renormalizes the effective Zeeman field, and the phase boundaries computed from the renormalized field reproduce the numerics.
This paper studies what happens to a one-dimensional topological insulator of ultracold fermionic atoms when a moire-like spatial modulation is imposed on the Zeeman field, and it reports two main fi…