Phonons in Twisted Transition Metal Dichalcogenide Bilayers (“Twistnonics”): Ultra-soft Phasons, and a transition from Superlubric to Pinned Phase

The tunability of the interlayer coupling by twisting one layer with respect to another layer of two-dimensional materials provide a unique way to manipulate phonons and related properties. We refer to this engineering of phononic properties as "Twistnonics". We study the effects of twisting on low-frequency shear (SM) and layer breathing (LBM) modes in transition metal dichalcogenide (TMD) bilayer using 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 “ultra-soft” phason modes (frequency ≤ 1 cm⁻¹) for any non-zero twist, corresponding to an effective translation of the moiré lattice by relative displacement of the constituent layers in a non-trivial way. Unlike the acoustic modes, the velocity of the phason modes is quite sensitive to twist angle. As twist angle decreases, (θ ≤ 3^° , & ≥ 57^°) the ultra-soft modes represent the acoustic modes of the “emergent” soft moiré scale lattice. Also, new high-frequency SMs appear, identical to those in stable bilayer TMD (θ = 0^°/60^°). 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 materials.