  Strain engineering can effectively tune the electronic, topological and
piezoelectric properties of materials. In this work, the small strain (-4\% to
4\%) effects on piezoelectric properties of $\alpha$-AsP monolayer are studied
by density functional theory (DFT). The piezoelectric stress tensors $e_{ij}$
and elastic stiffness tensors $C_{ij}$ are reported by using density functional
perturbation theory (DFPT) and finite difference method (FDM). It is found that
the Young's modulus of $\alpha$-AsP monolayer shows very strong anisotropy, and
the armchair direction is very softer than zigzag direction, which provides
possibility for tuning easily piezoelectric coefficients along the armchair
direction. In considered strain range, uniaxial compressive (tensile) strain
along the armchair (zigzag) direction is found to raise observably both the
$e_{22}$ and $d_{22}$ (absolute value). In fact, both compressive strain along
the armchair direction and tensile strain along the zigzag direction
essentially reduce the lattice constants along the armchair direction, which
can enhance the piezoelectric coefficients. The $e_{ij}$ of $\beta$-AsP
monolayer as a function of strain is also studied to illustrate the importance
of particular puckered structure of $\alpha$-AsP in enhancing the piezoelectric
coefficients. A classic SnSe monolayer with puckered structure is used to
further declare that small strain along the armchair direction can effectively
improve the piezoelectric coefficients. For example, the $d_{22}$ of SnSe
monolayer at -3.5\% strain is up to 628.8 pm/V from unstrained 175.3 pm/V. For
SnSe monolayer, a large peak is observed for $e_{22}$, which is due to a
structural phase transition. For $e_{16}$ of SnSe monolayer, a large peak is
also observed due to the cross of lattice constants $a$ along the zigzag
direction and $b$ along the armchair direction.
