Continuum model for the terahertz dielectric response of glasses

Abstract

Boson peak dynamics in glasses produce a robust crossover in the terahertz (THz) dielectric response that standard Debye or Lorentz models do not capture. We develop a continuum description of this THz response, coupling an infrared-effective charge fluctuation spectrum to a frequency-dependent shear modulus, and apply it to glycerol glass. The model reproduces the measured complex dielectric function and the nearly linear infrared light-vibration coupling around the boson peak, and highlights the dominant role of transverse shear dynamics.

Figures (8)

• Figure 1: Complex dielectric response of glycerol glass at $80~\mathrm{K}$. Symbols: THz-TDS measurements; solid curves: model. Plotted are $\varepsilon'(\omega)$ and $\varepsilon"(\omega)$ versus frequency (THz). The model reproduces the crossover from resonance-like behavior below $\omega_{\rm BP}$ to a broad Debye-like response above $\omega_{\rm BP}$. The weak convex-upward feature in $\varepsilon'(\omega)$ near $\omega_{\rm BP}$ is consistent with a shallow dip in $G'(\omega)$, i.e., a reduction of $V_{\rm TA}(\omega)=\sqrt{G'(\omega)/\rho}$ associated with the BP.
• Figure 2: Reduced spectra and IR light-vibration coupling. (a) Reduced absorption $\alpha(\omega)/\omega^{2}$ (blue symbols) obtained from Fig. \ref{['fig:fig1']} via $\alpha(\omega)=\omega\varepsilon"(\omega)/(c\,n'(\omega))$ (with $c$ the speed of light and $n'(\omega)$ the real part of the refractive index), together with the reduced VDOS $g(\omega)/\omega^{2}$ (orange symbols) from independent inelastic neutron scattering (INS) Wuttke1995; solid lines are the model. (b) $C_{\rm IR}(\omega)=\alpha(\omega)/g(\omega)$. The near-linear dependence around the BP is captured by the model, whereas the quadratic Taraskin form $A+B\omega^{2}$ does not capture this trend. Vertical dashed lines mark the BP positions from IR and INS, $\omega_{\rm BP\text{-}IR}/2\pi \approx 1.40~\mathrm{THz}$ and $\omega_{\rm BP\text{-}INS}/2\pi \approx 1.00~\mathrm{THz}$, respectively. Here $\nu$ denotes the linear frequency, $\nu=\omega/2\pi$.
• Figure 3: Static charge and density correlations in glycerol glass ($80~\mathrm{K}$). Shown are the charge--charge structure factor $S_{ZZ}(k)$ (blue) and the mass-density static structure factor $S_{\rho\rho}(k)$ (magenta) obtained from MD simulations. The FSDP and Debye wavenumbers ($k_{\rm FSDP}$, $k_{\rm D}$) are indicated. $S_{\rho\rho}(k)$ exhibits a pronounced FSDP at $k \sim 1.5~\text{\AA}^{-1}$, whereas $S_{ZZ}(k)$ has no FSDP maximum; instead its first (lowest-$k$) maximum appears only at higher $k$, on the interatomic-spacing scale.
• Figure 4: Evolution with $R=q_{0}/(q_{2}k_{\rm D}^{2})$ in $\Delta q(k)=q_{0}+q_{2}k^{2}$: approaching the Taraskin-like regime. For each $R$, $q_0$ and $q_2$ are rescaled to keep $\int_{0}^{k_{\mathrm{D}}} \! dk\, k^{2}\lvert \Delta q(k)\rvert^{2}$ constant, isolating the effect of the $k$-independent term $q_0$ (see Supplemental Material SM). (a) Normalized $\Delta q(k)$ (scaled to unity at $k=k_{\rm D}$) plotted as a function of $k/k_{\rm D}$ for several $R$. (b) Normalized $C_{\rm IR}(\omega)$ (scaled to unity at $2.5~\mathrm{THz}$) computed with the same $G(\omega)$. Increasing $R$ strengthens the $k$-independent part of $\Delta q(k)$ and drives $C_{\mathrm{IR}}(\omega)$ from a nearly linear form (small $R$) toward the Taraskin-like behavior $C_{\mathrm{IR}}(\omega)\simeq A + B\omega^{2}$.
• Figure S1: Transverse and longitudinal contributions to the modeled complex dielectric function. (a) Real part and (b) imaginary part. Red: transverse contribution $\varepsilon_T(\omega)$; blue: longitudinal contribution $\varepsilon_L(\omega)$; black: total $\varepsilon_T(\omega)+\varepsilon_L(\omega)=\varepsilon(\omega)-\varepsilon_\infty$. The functions $\varepsilon_T(\omega)$ and $\varepsilon_L(\omega)$ are defined in Eqs. (S35) and (S36).