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 of amorphous silicon and titanium dioxide, we find that their energy landscape is better represented by a connected network of inherent structures than a collection of isolated TLS. Each connection is a single energy barrier between two minima, and a network is connected if all states (minima) can be reached from any given state. 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 avenues and properties to analyze for the targeted design of low mechanical loss materials.