Coupling and Stacking Order of ReS$_{\mathrm{\mathbf{2}}}$\textbf{~Atomic Layers Revealed by Ultralow Frequency Raman Spectroscopy}

We investigate the ultralow-frequency Raman response of atomically thin ReS$_{\mathrm{2}}$, a special type of two-dimensional (2D) semiconductors with unique distorted 1T structure. Bilayer and few-layer ReS$_{\mathrm{2}}$~exhibit rich Raman spectra at frequencies below 50 cm$^{\mathrm{-1}}$, where a panoply of interlayer shear and breathing modes are observed. The emergence of these interlayer phonon modes indicate that the ReS$_{\mathrm{2}}$~layers are coupled and orderly stacked. Whereas the interlayer breathing modes behave similarly to those in other 2D layered crystals, the shear modes exhibit distinctive behavior due to the in-plane lattice distortion. In particular, the two shear modes in bilayer ReS$_{\mathrm{2}}$ are nondegenerate and clearly resolved in the Raman spectrum, in contrast to the doubly degenerate shear modes in other 2D materials. By carrying out comprehensive first-principles calculations, we can account for the frequency and Raman intensity of the interlayer modes and determine the stacking order in bilayer ReS$_{\mathrm{2}}$.