Discerning the Vibrational Nature of ReS₂ Raman Modes Using Solid-Angle-Resolved Raman Spectroscopy

Abstract

ReS2 exhibits reduced crystal symmetry, which leads to pronounced anisotropy and intricate Raman vibrations. However, to date, the vibrational nature of ReS2 Raman modes has remained elusive, with unresolved theoretical disputes. Here, we study Raman vibrations in ReS2 crystals using solid-angle-resolved Raman spectroscopy, which allows us to leverage the full 3 × 3 Raman tensor to resolve the Ag-like and Eg-like nature of all the 18 Raman modes. Combined with pressure-dependent measurements, we observe distinct behavior in the Ag-like and Eg-like modes. Our findings show unambiguous experimental evidence for discerning the ReS2 Raman modes and can offer important insights into the vibrational nature of Raman modes in layered anisotropic crystals.

Orientation–polarization dependence of pressure-induced Raman anomalies in anisotropic 2D ReS2

“…Compared with the reduced in-plane 2 × 2 tensor (black), the coefficients of c and e (red) are manifested in the full 3 × 3 tensor, representing the out-of-plane Raman vibrations and associated polarizability changes. Such facts can also be clearly seen from the calculated intensity: 13 I A g -like (H_ ‖ ) = a 1 2 , I E g -like (H_ ‖ ) = a 2 2 + d 2 I A g -like (H_⊥) = b 1 2 , I E g -like (H_⊥) = b 2 2 + d 2 I A g -like (V_ ‖ ) = a 1 2 , I E g -like (V_ ‖ ) = a 2 2 + e 2 I A g -like (V_⊥) = c 2 , I E g -like (V_⊥) = e 2 From the calculations above, we can see that the same pressure-induced phase transitions in the ReS 2 crystal could generate different pressure-dependent Raman features (appearance and disappearance) for the H and V configurations, originating from the different intensity expressions dominated by specific tensor elements: H ( a 1 , a 2 , b 1 , b 2 , and d ) and V ( a 1 , a 2 , c , and e ). These tensor elements show distinct responses to pressure, and thus the intensity evolution of the Raman mode is different between the H and V configurations.…”

“…We note that the birefringence effect does not apply to these four particular configurations (H_ ‖ , H_⊥, V_ ‖ , V_⊥). 13 The full 3 × 3 tensors ( R ) of the A g -like and E g -like modes in ReS 2 are given by 13 :Here, we use the full 3 × 3 tensor for analyzing the pressure effect on the tensor elements correlated with both H and V configurations. Compared with the reduced in-plane 2 × 2 tensor (black), the coefficients of c and e (red) are manifested in the full 3 × 3 tensor, representing the out-of-plane Raman vibrations and associated polarizability changes.…”

“…18,21 The vibrational frequency of the 18 A g modes is within the range of 100-450 cm À1 , where the 6 peaks below 250 cm À1 with a higher intensity are assigned to the lattice vibrations related to Re atoms, 7,18 and the other modes (above 250 cm À1 ) originate from the vibration of sulfur atoms. From our previous study, 13 we denote those modes with larger weights of in-plane (out-of-plane) vibration to be the E glike (A g -like) mode. 22,23 The assignment of the 18 Raman modes is summarized in Table S1 (ESI †).…”

“…8–11 By contrast, researchers have rarely explored anisotropy in ReS 2 crystals with the out-of-plane orientation, which could potentially give rise to attractive phenomena and delicate physics. 12,13…”

“…[8][9][10][11] By contrast, researchers have rarely explored anisotropy in ReS 2 crystals with the out-of-plane orientation, which could potentially give rise to attractive phenomena and delicate physics. 12,13 Meanwhile, pressure engineering is highly effective for tuning the symmetry and anisotropy in 2D crystals, and has led to the observation of intriguing physics such as phase transitions, 12 2D-3D structure transitions, 14 metallization, 15 and superconductivity. 16 In particular, pressure-induced anisotropy enhancement in ReS 2 crystals has recently been demonstrated.…”