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Department of Physics

The Cavendish Laboratory
Left: Benjamin Remez, Centre: Moire superlattice, at a twist angle of 9 degrees, Right: Danny Bennett

Danny Bennett and Benjamin Remez are two PhD students in the Theory of Condensed Matter group. Devising their project completely on their own, they have developed the first theoretical description of a big recent discovery in the field of 2D materials. 

We’ve caught up with Danny just as their results are being published in one of the Nature journals:  npj 2D Materials & Applications.


As theorists it is extremely important to relate our work to experiment, and there is no better feeling than seeing our original ideas being experimentally validated!Danny Bennett

Can you tell us in a few words what your paper is about? 

We have developed a theory addressing experimentally observed ferroelectricity in twisted systems, which was one of the biggest discoveries of the last two years in the field of 2D materials. In other words, the electric field changes the delicate balance between the binding energy and elastic energy, causing the structure to change and the charges to redistribute themselves.


Figure 1: Moiré superlattice, at a twist angle of 9 degrees. Illustration by Benjamin Remez.

Figure 2: Local polarization along the diagonal of a moiré superlattice. The asymmetric stacking configurations, sketched above, lead to a symmetry breaking and a nonzero polarization.


That sounds ground-breaking. Tell us more!

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 (see Fig. 1), and dramatically changing the physical properties.

In 2018, it was discovered that by twisting the layers in bilayer graphene by the `magic angle' of 1.05 degrees, the normally metallic system could exhibit superconducting and insulating behaviour, neither of which are possible when untwisted. Since then, twistronics has generated huge interest in the condensed matter physics community, and a wide range of additional phenomena have been attributed to moiré superlattices, such as magnetism, excitonic and topological behaviour.

In late 2020, twisted bilayer systems were reported to be ferroelectric when a perpendicular electric field was applied across them. 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 our paper, we 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 (see Fig. 2), which averages to zero. Moiré superlattices also undergo lattice relaxation in order to balance the stacking energy and the elastic energy coming from in-plane strains, resulting in sharp domain structures. When a field is applied, the local polarization changes the stacking energy and offsets this delicate balance. This causes the size of the domains to change (see Fig. 3), leading to a nonzero average polarization. The elastic energy is very sensitive to the twist angle, and hence the polar response is too, which agrees with experimental findings.

Figure 3: Lattice relaxation for bilayer MoS2 at a twist angle of θ= 0.2. At zero field there is a ∁6 symmetry and a sharp triangular structure. The electric field breaks this symmetry and the domains change continuously, eventually forming a sharp hexagonal structure.

This is the first theoretical description of a very big recent discovery in the field, and the work was done entirely by you and your co-author Benjamin Remez, both PhD students. This is a great achievement! Can you tell us a bit more about how you independently run this project with Benjamin?

I have been interested in 2D materials since a Summer internship during my undergraduate studies. During my PhD with Prof. Emilio Artacho, I moved on to study phase transitions and polarization in perovskites, these materials that have emerged as promising alternatives to silicon in the last decade.  

Alongside my PhD research, I was thinking about how ideas I encountered, such as polarization and electromechanical couplings, could manifest in 2D materials. I was regularly discussing these ideas with Benjamin Remez, who was studying excitons in 2D materials with his PhD supervisor Prof. Nigel Cooper.

Somewhere along the way our discussions snowballed into an independent research project, and before we knew it, we started to see experimental papers being published which were directly related to our ideas. As theorists it is extremely important to relate our work to experiment, and there is no better feeling than seeing our original ideas being experimentally validated!

Danny Bennett is a member of the CDT for computational methods for materials science.


Bennett, D., Remez, B, 'On electrically tunable stacking domains and ferroelectricity in moiré superlattices' npj 2D Mater Appl 6, 7 (2022). DOI:10.1038/s41699-021-00281-6