  The so-called interlayer-sliding ferroelectricity was recently proposed as an
unconventional route to pursuit electric polarity in van der Waals
multi-layers, which was already experimentally confirmed in WTe$_2$ bilayer
even though it is metallic. Very recently, another van der Waals system, i.e.,
the ZrI$_2$ bilayer, was predicted to exhibit the interlayer-sliding
ferroelectricity with both in-plane and out-of-plane polarizations [Phys. Rev.
B \textbf{103}, 165420 (2021)]. Here the ZrI$_2$ bulk is studied, which owns
two competitive phases ($\alpha$ \textit{vs} $\beta$), both of which are
derived from the common parent $s$-phase. The $\beta$-ZrI$_2$ owns a
considerable out-of-plane polarization ($0.39$ $\mu$C/cm$^2$), while its
in-plane component is fully compensated. Their proximate energies provide the
opportunity to tune the ground state phase by moderate hydrostatic pressure and
uniaxial strain. Furthermore, the negative longitudinal piezoelectricity in
$\beta$-ZrI$_2$ is dominantly contributed by the enhanced dipole of ZrI$_2$
layers as a unique characteristic of interlayer-sliding ferroelectricity, which
is different from many other layered ferroelectrics with negative longitudinal
piezoelectricity like CuInP$_2$S$_6$.
