  We derive an analytic formula for the Young's modulus in single-layer black
phosphorus using the valence force field model. By analyzing the directional
dependence for the Young's modulus, we explore the third principle direction
with direction angle phi_tp = 0.268pi besides armchair and zigzag directions.
The maximum Young's modulus value is in the third principle direction. More
specifically, the Young's modulus is 52.2 N/m, 85.4 N/m, and 111.4 N/m in the
armchair direction, zigzag direction, and the third principle direction,
respectively. This new principle direction is of significance for future
discussions of other anisotropic properties in the single-layer black
phosphorus.
