Moir\'e Ferroelectricity-Driven Band Engineering in Twisted Square Bilayers

TL;DR

This paper develops a moiré band theory for twisted square bilayers, revealing ferroelectricity as a new control mechanism for miniband engineering and identifying candidate materials with unique symmetry properties.

Contribution

It introduces a novel moiré band theory for twisted square bilayers and highlights ferroelectricity as an independent tuning parameter for miniband control.

Findings

Ferroelectricity enables switching between miniband regimes.

Emergent nonsymmorphic symmetry in momentum space.

Identification of Cu$_2$WS$_4$ and GeCl$_2$ as candidate materials.

Abstract

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 Cu$_2$WS$_4$ and GeCl$_2$ 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.