We develop the moir\'e band theory for M-valley twisted square homobilayers with layer groups P-42m and P-4m2, and propose candidate material realizations. We show that moir\'e ferroelectricity-originating from sliding ferroelectricity in the untwisted bilayers-provides an independent control knob for miniband engineering in addition to interlayer tunneling. The competition between these two effects enables controlled switching between layer-resolved bilayer minibands and an effective single isolated miniband. Remarkably, these systems exhibit an emergent momentum-space nonsymmorphic symmetry in the absence of external magnetic fields. Large-scale \emph{ab initio} calculations identify Cu2WS4 and GeCl2 as representative materials realizing the ferroelectricity- and tunneling-dominated regimes, respectively. Our results establish twisted square homobilayers as a promising platform for correlated band engineering beyond moir\'e hexagonal systems.
@article{arxiv.2603.15140,
title = {Moir\'e Ferroelectricity-Driven Band Engineering in Twisted Square Bilayers},
author = {Kejie Bao and Rui Shi and Huan Wang and Linghao Huang and Jing Wang},
journal= {arXiv preprint arXiv:2603.15140},
year = {2026}
}