Black phosphorus attracts enormous attention as a promising layered material for electronic, optoelectronic and thermoelectric applications. Here we report large anisotropy in in-plane thermal conductivity of single-crystal black phosphorus nanoribbons along the zigzag and armchair lattice directions at variable temperatures. Thermal conductivity measurements were carried out under the condition of steady-state longitudinal heat flow using suspended-pad micro-devices. We discovered increasing thermal conductivity anisotropy, up to a factor of two, with temperatures above 100 K. A size effect in thermal conductivity was also observed in which thinner nanoribbons show lower thermal conductivity. Analysed with the relaxation time approximation model using phonon dispersions obtained based on density function perturbation theory, the high anisotropy is attributed mainly to direction-dependent phonon dispersion and partially to phonon–phonon scattering. Our results revealing the intrinsic, orientation-dependent thermal conductivity of black phosphorus are useful for designing devices, as well as understanding fundamental physical properties of layered materials.

Although it has been qualitatively demonstrated that surface roughness can reduce the thermal conductivity of crystalline Si nanowires (SiNWs), the underlying reasons remain unknown and warrant quantitative studies and analysis. In this work, vapor-liquid-solid (VLS) grown SiNWs were controllably roughened and then thoroughly characterized with transmission electron microscopy to obtain detailed surface profiles. Once the roughness information (root-mean-square, σ, correlation length, L, and power spectra) was extracted from the surface profile of a specific SiNW, the thermal conductivity of the same SiNW was measured. The thermal conductivity correlated well with the power spectra of surface roughness, which varies as a power law in the 1-100 nm length scale range. These results suggest a new realm of phonon scattering from rough interfaces, which restricts phonon transport below the Casimir limit. Insights gained from this study can help develop a more concrete theoretical understanding of phonon-surface roughness interactions as well as aid the design of next generation thermoelectric devices.

In electrically conductive solids, the Wiedemann-Franz law requires the electronic contribution to thermal conductivity to be proportional to electrical conductivity. Violations of the Wiedemann-Franz law are typically an indication of unconventional quasiparticle dynamics, such as inelastic scattering, or hydrodynamic collective motion of charge carriers, typically pronounced only at cryogenic temperatures. We report an order-of-magnitude breakdown of the Wiedemann-Franz law at high temperatures ranging from 240 to 340 kelvin in metallic vanadium dioxide in the vicinity of its metal-insulator transition. Different from previously established mechanisms, the unusually low electronic thermal conductivity is a signature of the absence of quasiparticles in a strongly correlated electron fluid where heat and charge diffuse independently.