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

Co-existence of size-dependent and size-independent thermal conductivities in single layer black phosphorus