  The single-layer black phosphorus is characteristic for its puckered
structure, which has leaded to highly anisotropy in its optical, electronic,
and mechanical properties. We report, using the non-equilibrium Green's
function approach and the first-principles method, that the anisotropy in the
thermal conduction is very weak in the single-layer black phosphorus -- the
difference between two in-plane directions is less than 4%. Our phonon
calculations disclose that the two in-plane acoustic phonon branches have lower
group velocities in the direction perpendicular to the pucker, as the black
phosphorus is softer in this direction, leading to a weakening effect for the
thermal conductance in the perpendicular direction. However, the out-of-plane
acoustic phonon branch behaviors abnormally; i.e., the group velocity of this
phonon branch is higher in the perpendicular direction, although the
single-layer black phosphorus is softer in this direction. The abnormal
behavior of the out-of-plane phonon branch is closely related to the highly
anisotropic Poisson's ratio in the single-layer black phosphorus. As a result
of the counteraction between the in-plane phonon modes and the out-of-plane
phonon mode, the thermal conductance in the perpendicular direction is weaker
than the parallel direction, but the anisotropy is pretty small.
