Interplay of the interlayer distance and in-plane lattice relaxations in encapsulated twisted bilayers

Encapsulation protects functional layers, ensuring structural stability and improving the quality of assembled van der Waals heterostructures. Here, we develop a model that describes lattice relaxation in twisted bilayers accounting for encapsulation effects, incorporated via a single parameter characterizing the rigidity of encapsulation material interfaces. By analysing the twist-angle dependence of weak-to-strong lattice relaxation transition in twisted transition metal dichalcogenide bilayers, we show that increasing interface rigidity raises the crossover twist angle between the two relaxation regimes. Furthermore, tuning this rigidity parameter allows achieving good agreement with existing experimental results.