Anomalous interlayer vibrations in strongly coupled layered PdSe 2

In this work, we show unusual effects of strong interlayer coupling on low-frequency (LF) Raman scattering in exfoliated PdSe₂ crystals with different number of layers. Unlike many other layered materials, it is found that the measured frequencies of the breathing modes cannot be simply described by a conventional linear chain model (LCM) that treats each layer as a single rigid object. By using first-principles calculations, we show that strong deviations from layer rigidity can occur for the LF breathing vibrations of PdSe₂, which accounts for the observed disagreement with the conventional LCM. The layer non-rigidity and strong interlayer coupling could also explain the unusual strong intensities of the LF breathing modes that are comparable with those of the high-frequency Raman modes. These strong intensities allowed us to use a set of the measured LF Raman lines as unique fingerprints for a precise assignment of the layer numbers. The assignment of the layer numbers was further confirmed using second harmonic generation that appeared only in the noncentrosymmetric even-layer PdSe₂ crystals. In conclusion, this work thus demonstrates a simple and fast approach for the determination of the number of layers in 2D materials with strong interlayer coupling and non-rigid interlayer vibrations.