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The single-layer black phosphorus is characteristic for its puckeredstructure, which has leaded to highly anisotropy in its optical, electronic,and mechanical properties. We report, using the non-equilibrium Green'sfunction approach and the first-principles method, that the anisotropy in thethermal conduction is very weak in the single-layer black phosphorus -- thedifference between two in-plane directions is less than 4%. Our phononcalculations disclose that the two in-plane acoustic phonon branches have lowergroup velocities in the direction perpendicular to the pucker, as the blackphosphorus is softer in this direction, leading to a weakening effect for thethermal conductance in the perpendicular direction. However, the out-of-planeacoustic phonon branch behaviors abnormally; i.e., the group velocity of thisphonon branch is higher in the perpendicular direction, although thesingle-layer black phosphorus is softer in this direction. The abnormalbehavior of the out-of-plane phonon branch is closely related to the highlyanisotropic Poisson's ratio in the single-layer black phosphorus. As a resultof the counteraction between the in-plane phonon modes and the out-of-planephonon mode, the thermal conductance in the perpendicular direction is weakerthan the parallel direction, but the anisotropy is pretty small.

Thermal Conduction in Single-Layer Black Phosphorus: Highly Anisotropic?