  Two-dimensional materials tend to become crumpled according to the
Mermin-Wagner theorem, and the resulting ripple deformation may significantly
influence electronic properties as observed in graphene and MoS2. Here we
unveil by first-principles calculations a new, highly anisotropic ripple
pattern in phosphorene, a monolayer black phosphorus, where compression induced
ripple deformation occurs only along the zigzag direction in the strain range
up to 10%, but not the armchair direction. This direction-selective ripple
deformation mode in phosphorene stems from its puckered structure with coupled
hinge-like bonding configurations and the resulting anisotropic Poisson ratio.
We also construct an analytical model using classical elasticity theory for
ripple deformation in phosphorene under arbitrary strain. The present results
offer new insights into the mechanisms governing the structural and electronic
properties of phosphorene crucial to its device applications.
