Connected Network Model for the Mechanical Loss of Amorphous Materials

TL;DR

This paper introduces a connected network model for amorphous materials' mechanical loss, revealing complex interactions that challenge the traditional isolated TLS model and suggest new pathways for designing low-loss materials.

Contribution

The authors develop an analytically tractable network theory for amorphous solids' mechanical loss, incorporating connectivity effects overlooked by the TLS model.

Findings

Network connectivity reduces low-frequency dissipation via additional relaxation pathways.

Connectivity can increase dissipation due to a broad distribution of energy minima.

The model predicts different frequency profiles compared to the isolated TLS model.

Abstract

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.