  Both Nb$_3$Pd$_x$Se$_7$ and Ta$_4$Pd$_3$Te$_{16}$ crystallize in a monoclinic
point group while exhibiting superconducting transition temperatures as high as
$T_c\sim 3.5$ and $\sim 4.7 $ K, respectively. Disorder was claimed to lead to
the extremely large upper critical fields ($H_{c2}$) observed in related
compounds. Despite the presence of disorder and heavier elements, $H_{c2}$s in
Ta$_4$Pd$_3$Te$_{16}$ are found to be considerably smaller than those of
Nb$_3$Pd$_x$Se$_7$ while displaying an anomalous, non-saturating linear
dependence on temperature $T$ for fields along all three crystallographic axes.
In contrast, crystals of the latter compound displaying the highest $T_c$s
display $H_{c2}\propto (1-T/T_c)^{1/2}$, which in monolayers of transition
metal dichalcogenides is claimed to be evidence for an Ising paired
superconducting state resulting from strong spin-orbit coupling. This anomalous
$T$-dependence indicates that the superconducting state of Nb$_3$Pd$_x$Se$_7$
is quasi-two-dimensional in nature. This is further supported by a nearly
divergent anisotropy in upper-critical fields, i.e. $\gamma=
H_{c2}^{b}/H_{c2}^{a^{\prime}}$, upon approaching $T_c$. Hence, in
Nb$_3$Pd$_x$Se$_7$ the increase of $T_c$ correlates with a marked reduction in
electronic dimensionality as observed, for example, in intercalated FeSe. For
the Nb compound, Density functional theory (DFT) calculations indicate that an
increase in the external field produces an anisotropic orbital response, with
especially strong polarization at the Pd sites when the field is perpendicular
to their square planar environment. Therefore, DFT suggests the field-induced
pinning of the spin to the lattice as a possible mechanism for decoupling the
superconducting planes. Overall, our observations represent further evidence
for unconventional superconductivity in the Pd chalcogenides.
