Open problems in transport physics of ultrahigh-thermal conductivity materials

Recent searches of high-lattice thermal conductivity (κ_l) materials have explored size-dependent non-diffusive phonon transport in low-dimensional systems and pursued compound crystals with light and heavy elements. As a paradigm shift from past high-κ_l criteria that emphasize simple crystals made of light elements, the latter has led to ultrahigh-κ_l semiconducting boron arsenide (BAs) where a large phonon gap in such compounds limits three-phonon scattering and makes four-phonon processes unusually important. Frequent four-phonon scattering and consequently convergent κ_l have also been calculated in graphene because of numerous low-frequency flexural phonons, raising a question whether high-order lattice anharmonicity is sufficient to prevent graphene and carbon nanotubes from breaking the κ_l records of diamond and graphite due to weakened phonon hydrodynamics. Open problems have also remained on four-phonon processes in BAs, electron–phonon coupling effects in semiconductors and semimetals including θ-tantalum nitride with predicted high \({\upkappa }_{l}\) ${\mathrm{\kappa }}_l$ , and quantized lattice thermal conductance in nanowires and nanotubes.