  The non-axial reflection-asymmetric $\beta_{32}$ shape in some transfermium
nuclei with N=150, namely $^{246}$Cm, $^{248}$Cf, $^{250}$Fm, and $^{252}$No
are investigated with multidimensional constrained covariant density functional
theories. By using the density-dependent point coupling covariant density
functional theory with the parameter set DD-PC1 in the particle-hole channel,
it is found that, for the ground states of $^{248}$Cf and $^{250}$Fm, the
non-axial octupole deformation parameter $\beta_{32} > 0.03$ and the energy
gain due to the $\beta_{32}$ distortion is larger than 300 keV. In $^{246}$Cm
and $^{252}$No, shallow $\beta_{32}$ minima are found. The occurrence of the
non-axial octupole $\beta_{32}$ correlations is mainly from a pair of neutron
orbitals $[734]9/2$ ($\nu j_{15/2}$) and $[622]5/2$ ($\nu g_{9/2}$) which are
close to the neutron Fermi surface and a pair of proton orbitals $[521]3/2$
($\pi f_{7/2}$) and $[633]7/2$ ($\pi i_{13/2}$) which are close to the proton
Fermi surface. The dependence of the non-axial octupole effects on the form of
energy density functional and on the parameter set is also studied.
