  Thermal conductivity of single layer black phosphorus (BP) is investigated by
combining density functional calculations and Peierls-Boltzmann transport
equation. Differing from isotropic and divergent thermal conductivities in
two-dimensional graphene and MoS$_2$, an compelling co-existence of
size-dependent and size-independent thermal conductivities are discovered for
single layer BP along zigzag (ZZ) and armchair (AM) direction, respectively.
Besides, thermal conductivities in single layer BP are found to be highly
anisotropic because of orientation dependent group velocities, e.g., thermal
conductivities at 300 K are 83.5 and 24.3 W/m-K along ZZ and AM directions for
single layer BP with a size of 10 $\mu m$, respectively.
