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Splitting of interlayer shear modes and photon energy dependent anisotropic Raman response in $N$-layer ReSe$_2$ and ReS$_2$

We investigate the interlayer phonon modes in $N$-layer rhenium diselenide (ReSe$_2$) and rhenium disulfide (ReS$_2$) by means of ultralow-frequency micro-Raman spectroscopy. These transition metal dichalcogenides exhibit a stable distorted octahedral (1T') phase with significant in-plane anisotropy, leading to sizable splitting of the (in-plane) layer shear modes. The fan-diagrams associated with the measured frequencies of the interlayer shear modes and the (out-of-plane) interlayer breathing modes are perfectly described by a finite linear chain model and allow the determination of the interlayer force constants. Nearly identical values are found for ReSe$_2$ and ReS$_2$. The latter are appreciably smaller than but on the same order of magnitude as the interlayer force constants reported in graphite and in trigonal prismatic (2Hc) transition metal dichalcogenides (such as MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$, WSe$_2$), demonstrating the importance of van der Waals interactions in $N$-layer ReSe$_2$ and ReS$_2$. In-plane anisotropy results in a complex angular dependence of the intensity of all Raman modes, which can be empirically utilized to determine the crystal orientation. However, we also demonstrate that the angular dependence of the Raman response drastically depends on the incoming photon energy, shedding light on the importance of resonant exciton-phonon coupling in ReSe$_2$ and ReS$_2$.