Electrically tunable stacking domains and ferroelectricity in moire superlattices

It is well known that stacking domains form in moire superlattices due to the competition between the interlayer van der Waals forces and intralayer elastic forces, which can be recognized as polar domains due to the local spontaneous polarization in bilayers without centrosymmetry. We propose a theoretical model which captures the effect of an applied electric field on the domain structure. The coupling between the spontaneous polarization and field leads to uneven relaxation of the domains, and a net polarization in the superlattice at nonzero fields, which is sensitive to the moire period. We show that the dielectric response to the field reduces the stacking energy and leads to softer domains in all bilayers. We then discuss the recent observations of ferroelectricity in the context of our model.

Electrostatics and domains in ferroelectric superlattices

The electrostatics arising in ferroelectric/dielectric two-dimensional heterostructures and superlatitices is revisited here within a simplest Kittel model, in order to define a clear paradigmatic reference for domain formation. The screening of the depolarizing field in isolated ferroelectric or polar thin films via the formation of 180$^{circ}$ domains is well understood, whereby the width of the domains $w$ grows as the square-root of the film thickness $d$, following Kittels law, for thick enough films ($wll d$). This behavior is qualitatively unaltered when the film is deposited on a dielectric substrate, sandwiched between dielectrics, and even in a superlattice setting, with just a suitable renormalisation of Kittels length. As $d$ decreases, $w(d)$ deviates from Kittels law, reaching a minimum and then diverging onto the mono-domain limit for thin enough films, always assuming a given spontaneous polarization $P$ of the ferrolectric, only modified by linear response to the depolarizing field. In most cases of experimental relevance $P$ would vanish before reaching that thin-film regime. This is not the case for superlattices. Unlike single films, for which the increase of the dielectric constant of the surrounding medium pushes the deviation from the Kittels regime to lower values of $d$, there is a critical value of the relative thickness of ferroelectric/dielectric films in superlattices beyond which that behavior is reversed, and which defines the separation between strong and weak ferroelectric coupling in superlattices.