Topological entropy controls thermal conductivity in disordered carbon polymorphs

The structural and thermal properties of disordered carbon play a pivotal role in many diverse energy technologies: nanoporous carbon finds applications in batteries and supercapacitors; (defective) graphite serves as a moderator in nuclear reactors, where neutron irradiation causes structural changes and material's aging. Although experiments indicate a strong dependence of thermal conductivity on structural disorder, the fundamental relationship between atomistic structure and macroscopic conductivity remains unclear. Here we address this challenge, using the Wigner formulation of thermal transport, quantum-accurate machine-learning potentials, and real-space topological descriptors to shed light on how disorder in the atomic bond network affects thermal conductivity. We introduce a descriptor – topological entropy – which quantitatively captures the variability of local coordination environments, and we show that it correlates with thermal conductivity at a given density. Our research establishes disorder in the atomic bond topology as a fundamental degree of freedom to control and engineer thermal conductivity, calling for studies on how to practically control the local bonding topology. Finally, our findings also suggest the possibility to probe atomistic structural properties using thermal-conductivity measurements.