A contrastive investigation of the symmetry aspects of phonons in monolayer chromium trihalides and their Janus structures Y3-Cr2-X3 (X, Y = F, Cl, Br, I) by group theory is presented. We first classify all phonons at the Brillouin-zone center (Γ) into the irreducible representation. Then the infrared and Raman activity of optic phonons, Raman tensors, and the possible polarization assignments of R active phonons are predicted. Base on these results, we clarify the the discrepancy about the Raman activity o optic modes in monolayer CrI3. Besides, we find that the Raman and infrared spectra for X3-Cr2-X3 are exclusive, whereas that for Janus Y3-Cr2-X3 are coincident. This distinction is vital for optic spectra identification of Janus Y3-Cr2-X3 monolayer from X3-Cr2-X3 monolayer. In addition, we derive the symmetry-matched phonon eigenfunctions and corresponding schematic representations of the eigenvectors for both F3-Cr2-I3 and I3-Cr2-I3 monolayer, which demonstrate intuitively the origin of phonon chirality and magnetism. At last, our analysis indicates that the spin-phonon coupling, the magneto-optical effect of infrared and Raman active phonons, and phonon chirality should be observed in Janus Y3-Cr2-X3 monolayer as that and even easier than that in X3-Cr2-X3 monolayer. Our work provides a detailed guiding map for experimental characterization of Y3-Cr2-X3 monolayer, and also reveals important effects of optic phonons in Janus Y3-Cr2-X3 monolayer.
@article{arxiv.2204.06152,
title = {Group Theory Analysis of Phonons in Monolayer Chromium Trihalides and Their Janus Structures},
author = {Y. C. Liu and H. B. Niu and J. B. Lin and V. Wang},
journal= {arXiv preprint arXiv:2204.06152},
year = {2022}
}