Phonon frequency comb close to an isolated Einstein mode in InSiTe3

Abstract

The emergence of phonon frequency combs exemplifies a rare and intriguing phenomenon in quantum solids. Materials with distinctive phonon band structures are especially promising for hosting such states, as their vibrational dispersion landscape across the Brillouin zone can facilitate the formation of long-lived, collective lattice excitations. In the layered Van der Waals compound InSiTe$_3$, polarization-resolved Raman spectroscopy reveals a pronounced anharmonicity in symmetry-predicted modes and the formation of a self-organized frequency domain structure (coherent-like state), in the range of a localized highenergy A$_{1g}$ phonon mode near 500 cm$^{-1}$. This strong phonon-phonon coupling manifests itself as an anomalous temperature dependence around 200 K, coinciding with the appearance of higher-order excitations within the phonon density of states gap. These findings position InSiTe$_3$ as an unconventional platform where intrinsic highly structured phonon spectral correlations and unusually strong anharmonic effects coexist, opening new avenues for exploring emergent vibrational phenomena in low-dimensional materials.

Figures (8)

• Figure 1: SEM and EDS mapping of a freshly cleaved surface of an $\mathrm{InSi}\mathrm{Te}_{3}$ single crystal. The right part of the figure shows a flat surface over an extended area. The white rectangle indicates the area in which the EDS mapping was performed. The green, red, and turquoise areas on the left demonstrate the homogeneous distributions of the elements.
• Figure 2: Raman spectra of $\mathrm{InSi}\mathrm{Te}_{3}$ in parallel ($\theta = 0^{\circ}$) and cross ($\theta = 90^{\circ}$) polarization configurations at (a) 80 K and (b) 300 K. The orange lines represent the phenomenological continua (see text). Inset of (a) $\mathrm{InSi}\mathrm{Te}_{3}$ crystallographic unit cell with vectors of incident and scattered light polarizations ${\mathbf e}_{i}$ and ${\mathbf e}_{s}$, respectively. For symmetry reasons the orientation of the polarizations with respect to the crystal axes $a$ and $b$ is irrelevant. Inset of (b) displacement pattern of $A1g^{(3)}$ mode. The arrow lengths are proportional to the square root of the inter-atomic forces. For this mode only the Si atoms move.
• Figure 3: (a)-(c) Phonon excitations modeled with Voigt profiles in parallel ($\theta = 0^{\circ}$) polarization configuration where phonons of both A1g and Eg symmetry are observed. The spectra are recorded at 80 K.
• Figure 4: Temperature dependences of the energies and Lorentzian linewidths of the $A1g^{(1)}$ and $A1g^{(2)}$ phonons. There are discontinuities of both the energies and linewidths close to 200 K. The dashed lines represent fits to the data below 200 K. The linewidths and energies are well described by anharmonic phonon decay (Eq. \ref{['eq:Anharmonic']}) and thermal expansion, respectively.
• Figure 5: Raman spectra in the range between 80 $\rm cm^{-1}$ and 350 $\rm cm^{-1}$ at temperatures as indicated. The overtone excitations increase abruptly between 200 and 220 K in intensity. Inset: Calculated phonon dispersion along the high-symmetry directions as indicated and PDOS. The shaded area marks the gap in the PDOS.