Chiral phonons in sixfold chiral CrSi$_2$: Raman spectroscopy and first-principles calculations

Abstract

Chiral phonons have been identified in several chiral crystals, primarily in those with trigonal symmetry and threefold screw axes. In this study, chiral phonons in CrSi$_2$, a chiral crystal with a sixfold helical structure, were investigated. Circularly polarized Raman spectroscopy revealed a subtle splitting of doubly degenerate $E_2$ phonon modes between cross-circular polarization configurations. These observations, supported by first-principles phonon calculations, indicate the presence of chiral phonons in CrSi$_2$, expanding the scope of materials that exhibit chiral vibrational modes beyond the conventional trigonal class.

Figures (9)

• Figure 1: Crystal structures of CrSi2: (a) L- and R-CrSi2, which are mirror images of each other, and (b) sixfold crystal structure viewed along the $c$-axis.
• Figure 2: Stokes Raman spectra and phonon mode assignments for the L-CrSi2 crystal: vertical offsets have been added for clarity. The inset shows the RL configuration. Here, R and L are defined as the direction of polarization rotation in the sample plane, irrespective of the propagation direction.
• Figure 3: Stokes spectra of the four $E_2$ modes of (a--d) L- and (e--h) R-CrSi2 in cross-circular polarization configurations: (a), (e) $E_2^{(1)}$, (b), (f) $E_2^{(2)}$, (c), (g) $E_2^{(3)}$, and (d), (h) $E_2^{(4)}$ peaks, showing polarization-dependent energy splittings.
• Figure 4: (a) CAM $m$ and (b) the $z$ component of the angular momentum $L_z$ for phonons in L-CrSi2: the CAM values $m=-2,\, -1,\, 0,\, +1,\, +2$, and $3$ are shown in blue, sky blue, green, yellow, red, and black, respectively.
• Figure 5: Schematic illustration of Raman selection rules: (a) anti-Stokes and (b) Stokes processes. $\ket{g}$ denotes the ground state, while $\ket{m}$ represents an intermediate state involved in the Raman transitions and $\ket{v_{+(-)}}$ represents an excited state with CAM $m=\pm2$ phonons. In this schematic, the incident and scattered photons carry CAM $\sigma_{\mathrm{i}}=-1$ and $\sigma_{\mathrm{s}}=+1$, respectively (LR configuration), resulting in $m=+2$ for the Stokes process and $m=+2$ for the anti-Stokes process.