Mismatch between Raman shear modes and ferroelectric polarization in 3R-MoS$_{2}$
Sliding ferroelectricity in parallel-stacked two-dimensional van der Waals materials enables a broad range of novel device concepts, but exploiting it requires reliable, non-destructive assignment of the underlying stacking order and polarization state. Here, we combine Kelvin-probe force microscopy (KPFM) with low-frequency Raman spectroscopy to probe the polarization domains and stacking configurations of a exfoliated trilayer 3R-MoS$_{2}$ flake on a hBN substrate. We find that ABA and BAB - both stackings with zero net polarization - are indistinguishable in KPFM, yet show drastically different low-frequency shear modes. This observation is reproduced across multiple flakes and is corroborated by low-temperature photoluminescence. Notably, the standard bond-polarizability model does not account for the difference in shear-mode activity between the ABA and BAB configurations, indicating that the interlayer Raman response of these stackings is governed by physics beyond a simple polarizability picture. Our results show that none of the here-used individual techniques alone is sufficient to assign sliding-ferroelectric stacking order and motivate a combined spectroscopic-scanning-probe approach.