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Abstract

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 first consider the large-angle limit which can be treated perturbatively and from which we obtain scaling laws for the atomic displacement field that allows one to extract relaxation parameters from ab-initio calculations [1]. For smaller angles, marked by the formation of a soliton network separating domains with near constant stacking, perturbation theory fails, and we need a different approach. By matching the exact solution of an isolated soliton near the domain walls, we obtain accurate expressions for the displacement field 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 our perturbative results for the displacement field, we obtain expressions for the moiré tunneling amplitudes as a function of twist angle, as well as for 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 "elastic screening" by optical lattice deformations not captured by continuum elasticity, and which has important 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).