Fig. 2. Polaronic character of exciton dynamics in bilayer CrI₃.

a Raman spectrum of bilayer CrI₃ acquired in the linearly crossed polarization channel at 40 K using a 633 nm laser. Insets show 1st-order single-phonon modes (linear parallel/crossed, i.e., XX/XY, channel in blue/red), 2nd-order two-phonon modes, and 3rd order three-phonon modes. The red arrow indicates the Raman-inactive longitudinal optical (LO) phonon frequency of importance, ${\omega }_{\mathrm{LO}}$. The spectral intensities in the frequency range above 118 cm⁻¹ are scaled by a factor of 0.1. b Zoom-in of the orange shaded area in the spectrum in a. The solid orange line overlaid on the raw data is the fit to the periodic pattern in the Raman spectrum with a sum of eight Lorentzian profiles indexed from N = 1 to N = 8 and a constant background, i.e., ${\sum }_{N=1}^8\frac{A_N{\left(\frac{{\mathrm{\Gamma }}_N}{2}\right)}^2}{{\left(\omega -{\omega }_N\right)}^2+{\left(\frac{{\mathrm{\Gamma }}_N}{2}\right)}^2}+C$. c Fit of the Raman spectrum over the 1st-order spectral range without (upper panel) and with (lower panel) the consideration of the N = 1 broad mode (shaded Lorentzian profile in the lower panel). d Plot of the fitted central frequency (${\omega }_N$) of the Nth Lorentzian profile in data taken at 40 K (solid orange triangle) and 290 K (hollow blue triangle). Dashed line is a linear fit (${\omega }_N=N{\omega }_{\mathrm{LO}}$) to the plot that yields a slot of ${\omega }_{\mathrm{LO}}=120.6\pm 0.9$ cm⁻¹. Inset shows the atomic displacement of the LO phonon mode.