Low-Frequency Raman Active Modes of Twisted Bilayer MoS$_2$

We study the low-frequency Raman active modes of twisted bilayer MoS2for several twist angles using a force-field approach and a parametrized bond polarizability model. We show that twist angles near high-symmetry stacking configurations exhibit stacking frustration that leads to significant buckling of the moiré superlattice. We find that atomic relaxation due to the twist is of prime importance. The periodic displacement of the Mo atoms shows the realization of a soliton network, and in turn, leads to the emergence of a number of frequency modes not seen in the high-symmetry stacking systems. Some of the modes are only seen in theXZRaman polarization setup while others are seen in theXYsetup. The symmetry of the normal modes, and how this affects the Raman tensors is examined in detail.