Phonons in twisted transition-metal dichalcogenide bilayers: Ultrasoft phasons and a transition from a superlubric to a pinned phase

The tunability of the interlayer coupling by twisting one layer with respect to another layer of two-dimensional materials provides a unique way to manipulate the phonons and related properties. We refer to this engineering of phononic properties as twistnonics. We study the effects of twisting on low-frequency shear modes (SMs) and layer breathing modes in a transition-metal dichalcogenide (TMD) bilayer using atomistic classical simulations. We show that these low-frequency modes are extremely sensitive to twisting and can be used to infer the twist angle. We find ultrasoft phason modes (frequency less than or similar to 1 cm(-1), comparable to acoustic modes) for any nonzero twist, corresponding to an effective translation of the moire lattice by relative displacement of the constituent layers in a nontrivial way. Unlike the acoustic modes, the velocity of the phason modes are quite sensitive to the twist angle. Also, high-frequency SMs appear for small twist angles, identical to those in stable bilayer TMD (theta = 0 degrees or 60 degrees), due to the overwhelming growth of stable stacking regions in relaxed twisted structures. Our study reveals the possibility of an intriguing theta-dependent superlubric to pinning behavior and of the existence of ultrasoft modes in all two-dimensional materials.