Probing the charge density wave transition in semimetallic 1 T − TiSe 2 − δ by temperature-dependent Raman spectroscopy

We present temperature-dependent Raman spectra of semimetallic $1{\mathrm{T}\text{\ensuremath{-}}\mathrm{TiSe}}_{2\ensuremath{-}\ensuremath{\delta}}$ single crystals from 10 to 300 K using a 532 nm excitation laser, probing the charge density wave (CDW) transition at 170 K. The first-order ${E}_{g}$ and ${A}_{1g}$ phonon modes exhibit asymmetric lineshapes above 170 K, which are described by the Breit--Wigner--Fano (BWF) function and become Lorentzian below 134 K. The Bose--Einstein anharmonic model reveals anomalies in the ${E}_{g}$ phonon peak position near the CDW transition, whereas the ${A}_{1g}$ mode follows conventional anharmonic behavior. Moreover, we observe six low-frequency Raman peaks between 84 and $123\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$, as well as one Raman peak at $295\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$. By comparing these features with the one-phonon and two-phonon density of states obtained from the first-principles calculations, we assign the low-frequency modes to defect-induced double-resonance Raman peaks and the $295\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ mode to a two-phonon double-resonance Raman peak. The first-principles calculations also indicate phonon softening near the M and L points in the Brillouin zone, suggesting the lattice instability associated with the CDW transition. Our results provide Raman fingerprints of the CDW transition and highlight the role of electron--phonon interactions in semimetallic $1{\mathrm{T}\text{\ensuremath{-}}\mathrm{TiSe}}_{2\ensuremath{-}\ensuremath{\delta}}$.