Low frequency modes in twisted flatland: Ultra-soft modes, superlubricity to strong pinning

Abstract

We study the effects of twisting on low frequency shear (SM) and layer breathing (LBM) modes in bilayer MoS2 using fully atomistic classical simulations. We show that these low frequency modes are extremely sensitive to twist and can be used to infer the twist angle. We find unique optical “ultra-soft” SMs (frequency< 1 cm− 1) for any non-zero twist, corresponding to an effective translation of the moiré superlattice by relative displacement of the constituent layers in a nontrivial way. Additionally, for small twists (θ≲ 3◦,≳ 57◦) new high-frequency SMs appear identical to those in stable bilayer MoS2 (θ= 0◦/60◦) due to the overwhelming growth of stable stacking regions in relaxed twisted structures. Our study reveals the possibility of an intriguing, θ dependent superlubric to pinning behavior and of the existence of ultra-soft modes in all two-dimensional (2D) materials, which can be used to controllably tune physical properties.