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We report a comparative study of rigid layer Raman-active modes in $N$-layer transition metal dichalcogenides. Trigonal prismatic (2Hc, such as MoSe$_2$, MoTe$_2$, WS$_2$, WSe$_2$) and distorted octahedral (1T', such as ReS$_2$ and ReSe$_2$) phases are considered. The Raman-active in-plane interlayer shear modes and out-of-plane interlayer breathing modes appear as well-defined features with wavenumbers in the range 0-40~cm$^{-1}$. These rigid layer modes are well-described by an elementary linear chain model from which the interlayer force constants are readily extracted. Remarkably, these force constants are all found to be of the same order of magnitude. Finally, we show that the prominent interlayer shear and breathing mode features allow high-precision hyperspectral Raman imaging of $N-$layer domains within a given transition metal dichalcogenide flake.

Hybrid heterostructures based on bulk GaN and two-dimensional (2D) materials offer novel paths toward nanoelectronic devices with engineered features. Here, we study the electronic properties of a mixed-dimensional heterostructure composed of intrinsic n-doped MoS2 flakes transferred on p-doped GaN(0001) layers. Based on angle-resolved photoemission spectroscopy (ARPES) and high resolution x-ray photoemission spectroscopy (HR-XPS), we investigate the electronic structure modification induced by the interlayer interactions in MoS2/GaN heterostructure. In particular, a shift of the valence band with respect to the Fermi level for MoS2/GaN heterostructure is observed, which is the signature of a charge transfer from the 2D monolayer MoS2 to GaN. The ARPES and HR-XPS revealed an interface dipole associated with local charge transfer from the GaN layer to the MoS2 monolayer. Valence and conduction band offsets between MoS2 and GaN are determined to be 0.77 and −0.51eV, respectively. Based on the measured work functions and band bendings, we establish the formation of an interface dipole between GaN and MoS2 of 0.2 eV.