Layer-dependent atomic relaxation in twisted multilayer moiré systems

Beyond bilayer moiré systems, twisted multilayer systems are emerging as platforms for studying correlated electron physics with greater tunability. A key step in developing interacting theories is to incorporate the effect of atomic relaxation, ensuring reliable single-particle models on which interacting models can be built. In this work, we develop an analytical theory for relaxation in multilayer moiré systems and observe that the layer degree of freedom plays a crucial role, as these systems exhibit a non-uniform degree of relaxation across the out-of-plane direction.