Ferroelectric materials have a spontaneous electric polarization that can be switched by an applied field. Traditionally, ferroelectricity requires a crystal structure with broken inversion symmetry — specific atomic arrangements where positive and negative charges don't balance locally. The chemistry dictates the electric order.
In twisted square bilayers, the twist alone is sufficient.
Take two layers of a centrosymmetric material — one that has no ferroelectricity whatsoever in its bulk form — and rotate them by a small angle. The moiré pattern created by the misalignment breaks inversion symmetry locally. Within each moiré unit cell, the stacking arrangement varies smoothly from one registry to another, and some of these registries have a net out-of-plane dipole moment. The result: a ferroelectric polarization that exists because of geometry, not chemistry.
The polarization then reaches back into the electronic structure. The electric field from the ferroelectric pattern shifts the on-site energies differently at different points in the moiré cell, reshaping the electronic bands. Flat bands — which host correlated electronic phases — can be tuned by switching the ferroelectric state. The mechanical arrangement produces the electric order, and the electric order produces the band engineering.
The switchability is the remarkable part. In a conventional ferroelectric, switching requires moving atoms — overcoming energy barriers set by the crystal structure. In the moiré ferroelectric, switching requires changing the interlayer charge distribution, which can be done with modest electric fields because the moiré stacking domains are soft. The switching energy is set by the moiré, not by atomic bonds.
No atoms move. The twist is fixed. What switches is the charge distribution within the moiré cell — a purely electronic reconfiguration within a geometrically imposed landscape.