Continuum model for the terahertz dielectric response of glasses

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.

💡 Research Summary

The paper addresses a long‑standing puzzle in the physics of glasses: the pronounced crossover in the terahertz (THz) dielectric response that occurs around the Boson peak (BP). While the reduced vibrational density of states g(ω)/ω^{D‑1} exhibits a universal excess at frequencies of a few THz, standard dielectric models—Debye (pure relaxation) and Lorentz (pure resonance)—fail to capture the experimentally observed transition from a resonance‑like response below ω_BP to a Debye‑like, broad relaxation above ω_BP. The authors therefore construct a continuum theory that explicitly couples an infrared‑effective charge‑fluctuation spectrum Δq(k) to a frequency‑dependent complex shear modulus G(ω).

Starting from the isotropic elastic equation of motion for the displacement field u(r,ω) driven by a uniform electric field E(ω), they decompose the dynamics into longitudinal (L) and two degenerate transverse (T₁,T₂) acoustic branches. Each branch obeys a harmonic‑oscillator‑type equation with a stiffness C_α(ω)k² (C_L = K+4/3 G, C_T = G) and a driving term proportional to Δq(k)E_α(ω). By averaging over disorder and polarization directions, they derive an analytic expression for the complex dielectric function ε(ω) (Eqs. 3–4). The key ingredients are: (i) the variance of the charge‑fluctuation spectrum ⟨|Δq(k)|²⟩_dis, which they approximate as a low‑order Maclaurin expansion Δq(k)≈q₀+q₂k², and (ii) the complex shear modulus G(ω) obtained from a heterogeneous‑elasticity‑theory coherent‑potential‑approximation (HET‑CPA) fit to the measured vibrational density of states.

The model is applied to glycerol glass at 80 K, a prototypical hydrogen‑bonded glass. Experimental THz‑time‑domain spectroscopy (THz‑TDS) provides the real and imaginary parts of ε(ω) over 0.2–2.5 THz. The authors fix q₀≈0 (the data are insensitive to a constant term) and determine q₂ by minimizing the misfit between calculated and measured ε′(ω) and ε″(ω). With the parameters listed in Table I, the calculated ε(ω) reproduces the measured spectra with high fidelity. Below ω_BP the response shows a Lorentz‑type resonance, while above ω_BP the dielectric loss broadens into a Debye‑like relaxation, exactly as observed experimentally. A subtle “convex‑up” bump in ε′(ω) near ω_BP is traced to a shallow dip in the storage modulus G′(ω), i.e., a reduction of the transverse sound speed V_TA(ω)=√