Upper limit of thermal conductivity in matter

Establish a rigorous physical upper bound on thermal conductivity in matter by determining the maximal attainable thermal conductivity across materials and the conditions under which it is achieved.

Background

The paper addresses a longstanding question in materials science concerning the maximum possible thermal conductivity achievable in materials. Historically, diamond has been regarded as the benchmark for extreme thermal conductivity, but a definitive upper bound has not been proven, owing to the complexity of phonon transport and multiple scattering mechanisms.

Using deep learning–accelerated crystal structure prediction and high-throughput Boltzmann transport calculations, the authors performed an extensive search over hundreds of thousands of inorganic crystalline structures. They confirm that diamond sets the upper bound within their explored space and argue it is very likely the overall limit at ambient conditions. Nonetheless, a formal, rigorous bound remains unestablished, motivating the explicit open problem stated in the abstract.