Connected Network Model for the Mechanical Loss of Amorphous Materials

Dissipation in amorphous solids at low frequencies is commonly attributed to activated transitions of isolated two-level systems (TLS) that come in resonance with elastic or electric fields. Materials with low mechanical or dielectric loss are urgently needed for applications in gravitational wave detection, high precision sensors, and quantum computing. Using atomistic modeling, we explore the energy landscape of amorphous silicon and titanium dioxide, and find that the pairs of energy minima that constitute single TLS form a sparsely connected network with complex topologies. Motivated by this observation, we develop an analytically tractable theory for mechanical loss of the full network from a nonequilibrium thermodynamic perspective. We demonstrate that the connectivity of the network introduces new mechanisms that can both reduce low frequency dissipation through additional low energy relaxation pathways, and increase dissipation through a broad distribution of energy minima. As a result, the connected network model predicts mechanical loss with distinct frequency profiles compared to the isolated TLS model. This not only calls into question the validity of the TLS model, but also gives us many new avenues and properties to analyze for the targeted design of low mechanical loss materials.

💡 Research Summary

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The paper challenges the long‑standing two‑level‑system (TLS) picture of low‑frequency mechanical loss in amorphous solids by showing that the underlying energy landscape is better described as a sparsely connected network of inherent structures (local minima) linked by transition barriers. Using atomistic simulations of amorphous silicon (a‑Si) and amorphous titanium dioxide (a‑TiO₂), the authors identify thousands of minima and the saddle points that connect them via nudged elastic band calculations. The resulting graphs are highly heterogeneous: only a few‑tenths of a percent of the possible edges are present, the degree distribution follows a power‑law, and many closed loops (cycles) appear, indicating a scale‑free, globally connected network rather than isolated pairs of states.

To translate this structural picture into a quantitative theory of mechanical loss, the authors adopt a nonequilibrium thermodynamic framework. They write the total energy as the sum of the elastic energy of an externally driven acoustic wave and the internal energy of the network. The strain couples linearly to the energies of the inherent structures, introducing a coupling vector Γ. The dynamics of occupation probabilities for each node are governed by a master equation with a transition‑rate matrix R(t) that obeys Arrhenius kinetics (rates ∝ exp