Fig. 1. (Color online) Structure of several 2DMs (graphene, TMDs and hBN) and related vdWHs, such as twisted bilayer MoS and twisted bilayer graphene with twisted angle , MoS /Graphene and WS /hBN heterostructure.

Fig. 2. (Color online) (a) Optical contrast of a flake comprising a t(1+1)LG and a t(1+3)LG^[7]. (b) Raman spectra in the spectral range of the C, LB and G modes for t(1+3)LG. Polarized Raman spectra are also shown to identify the C and LB modes^[8]. (c) Experimental (Exp., open diamonds) and theoretical (Theo., crosses) (C ) in t(m + n)LGs. The insert shows a schematic diagram of a linear chain model for t(2+3)LG including a bulk-like interlayer force constant , interfacial force constant and the force constant for the layers adjacent to the interface^[7].

Fig. 3. (Color online) (a) The reciprocal lattice of t2LM with = and schematic diagram of moiré basic vectors ( , i = 1,2,3) with . Red dashed and green solid lines correspond to the BZ of moiré and crystallographic superlattice of the t2LMs, respectively. (b) Raman spectra of 3R- and 2H-2LMs and t2LMs with different in the low-frequency region excited by E = 2.54 eV. (c) Raman spectra of 2LMs with different and monolayer MoS . Different shapes and color symbols represent the Raman modes from corresponding phonon branches. (d, e) The comparison of calculated and experimental frequencies of moiré phonons dependent on and ^[13].

Fig. 4. (Color online) (a) Raman spectra of 2LM/nLG in the S and LB peak spectral ranges. (b) Schematic diagram of a linear chain model (LCM) for the LB modes in 2LM/3LG, in which the next nearest LB coupling in the 3LG constituent is considered. (c) Pos(LB ) dependent on of the nLG constituent. The solid lines show the theoretical trend of Pos(LB ) on based on the improved LCM^[29].

Fig. 5. (Color online) (Color online) (a) Schematic diagram for constituent-vdWHs EPC of the LB modes in hBN/WS₂ vdWHs, and Raman spectra of a 39L-hBN/3LW in the region of 5–50 cm^–1. The triangles represent the expected LB modes in the 39L-hBN/3LW based on the LCM. (b) The modulus square of the projection from wavefunction of different LB modes in 39L-hBN/3LW vdWH onto the wavefunction of the LB mode in a standalone 3LW flake. (c) The relative intensity of LB modes in 39L-hBN/3LW vdWH based on the interlayer bond polarizability mode^[24].