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Theory of ferroelectric-like response in twisted 2D bilayers

Daniel Bennett and Benjamin Remez

The authors present a theory of electrically tunable lattice relaxation in twisted bilayer systems which explains the recent experimentally observed ferroelectric behaviour.

An applied electric field leads to uneven lattice relaxation in moiré superlattices, resulting in an average polarization.

Twistronics is the study of layered systems where the individual layers are twisted with respect to one another, leading to an interference pattern known as a moiré superlattice, and dramatically changing the physical properties. A wide range of additional phenomena have been attributed to moir\'e superlattices, such as superconductivity, metal-insulator transitions, magnetism, excitonic and topological behaviour. In late 2020, ferroelectricity was reportedly observed in twisted bilayer systems when a perpendicular electric field was applied. This ferroelectricity was highly unusual: the strength of the response appeared to be sensitive to the twist angle, it could be observed in metallic bilayers, and both continuous and discontinuous ferroelectric responses were observed in separate experiments. However, the underlying physical mechanism was not understood.

In their paper, Bennett and Remez propose that the electric field affects the lattice relaxation which occurs in moiré superlattices, leading to changes in the atomic structure and a nonzero average polarization. Most two-dimensional materials are typically thought of as nonpolar, but twisted systems actually have a local polarization, arising from the different stacking arrangements breaking inversion symmetry, which averages to zero. Moir\'e superlattices undergo lattice relaxation in order to balance the stacking energy, arising from interlayer van der Waals interactions, and the elastic related to the in-plane strain fields. This leads to the formation of sharp domain structures. When a field is applied, the local polarization changes the stacking energy and offsets this delicate balance. This causes the relative size of neighbouring domains to change, leading to a nonzero average polarization. The elastic energy, and hence the polar response, is very sensitive to the twist angle, which agrees with experimental findings.

On electrically tunable stacking domains and ferroelectricity in moiré superlattices D Bennett and B Remez, npj 2D Mater Appl 6, 7 (2022)

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