Physics Theory Seminar with Christophe De Beule on Lattice relaxation in twisted bilayer moirés

Atomic reconstruction in moiré materials can strongly modify their electronic properties, especially in moirés made from transition metal dichalcogenides which are the subject of intense current research. Hence, a theory of lattice relaxation in moirés that goes beyond numerical solutions, and how it modifies the electronic theory, is highly desirable.

In this talk, we present analytical results for atomic relaxation in twisted homobilayers with D6 and D3 symmetry, e.g. twisted bilayer graphene and twisted bilayer transition metal dichalcogenides. We will first discuss how lattice relaxation is constrained by the symmetry of the moiré. We then consider the perturbative regime ("large" twist angles) and obtain scaling laws for the large-angle behavior of the atomic displacement field that allows one to extract theory parameters from density-functional or molecular-dynamics simulations [1]. We take a different approach for the non-perturbative regime ("small" twist angles) which is marked by the formation of a soliton network separating domains with near constant stacking. By fitting the exact solution of an isolated soliton, we obtain accurate expressions for the displacement field in this limit that agree well with molecular-dynamics simulations [2].

Finally, we demonstrate how the moiré potentials in the electronic theory are modified in the presence of lattice relaxation, using twisted bilayer graphene as an example. With our results for the displacement field, we obtain expressions for the moiré tunneling amplitudes as a function of twist angle, as well as the pseudogauge fields due to relaxation-induced strain. In particular, we show that the magnitude of the latter was overestimated by one order of magnitude in the literature. This effect is due to "elastical screening" by optical lattice deformations not captured by continuum elasticity, which has wide implications for the field of straintronics beyond moiré materials [3].

[1] Mohammed M. Al Ezzi, Gayani N. Pallewela, Christophe De Beule, E. J. Mele, and Shaffique Adam. Phys. Rev. Lett. 133, 266201 (2024).
[2] Christophe De Beule, Gayani N. Pallewela, Mohammed M. Al Ezzi, Liangtao Peng, E. J. Mele, and Shaffique Adam. arXiv:2503.19162.
[3] Christophe De Beule, Robin Smeyers, Wilson Nieto Luna, E. J. Mele, and Lucian Covaci. Phys. Rev. Lett. 134, 046404 (2025).
 

This lecture was made possible by the William C. Ferguson Fund.