  For two-dimensional (2D) materials, a pure large out-of-plane piezoelectric
response, compatible with the nowadays bottom/top gate technologies, is highly
desired. In this work, the piezoelectric properties of penta-graphene (CCC)
monolayer are studied with pure out-of-plane piezoelectric effect by density
functional theory (DFT). However, the $d_{36}$ is very small, and only -0.065
pm/V. Two strategies are proposed to enhance piezoelectric properties of CCC
monolayer. Firstly, both biaxial and uniaxial strains are applied, but the
enhancement is very small, and at -2\% biaxial (-4\% uniaxial) strain, the
$d_{36}$ is increased only by 3.1\% (13.9\%). Secondly, a Janus penta-monolayer
(CCB) is constructed by replacing the top C (B) atomic layer in monolayer CCC
[pentagonal $\mathrm{CB_2}$ monolayer (CBB)] with B (C) atoms, which shows
dynamic and mechanical stability. Fortunately, the pure out-of-plane
piezoelectric effect of CCB monolayer still holds, and exhibits a band gap. The
calculated $d_{31}$ and $d_{32}$ are -0.505 pm/V and 0.273 pm/V, respectively,
which are very larger than $d_{36}$ of CCC monolayer. The out-of-plane
piezoelectricity $d_{31}$ of CCB monolayer is obviously higher compared with
many other 2D known materials. Moreover, its room-temperature electronic
mobility along y direction is as high as 8865.23 $\mathrm{cm^2V^{-1}s^{-1}}$.
Our works provide a new way to achieve pure out-of-plane piezoelectric effect,
which is highly desirable for ultrathin piezoelectric devices.
