  Layered heterostructure materials with two different functional building
blocks can teach us about emergent physical properties and phenomena arising
from interactions between the layers. We report the intergrowth compounds
KLa$M$$_{1-x}$Te$_{4}$ ($M$ = Mn, Zn; $x\approx$ 0.35) featuring two chemically
distinct alternating layers [LaTe$_3$] and [K$M$$_{1-x}$Te]. Their crystal
structures are incommensurate, determined by single X-ray diffraction for the
Mn compound and transmission electron microscope (TEM) study for the Zn
compound. KLaMn$_{1-x}$Te$_{4}$ crystallizes in the orthorhombic superspace
group $Pmnm$(01/2${\gamma}$)$s$00 with lattice parameters $a$ = 4.4815(3)
{\AA}, $b$ = 21.6649(16) {\AA} and $c$ = 4.5220(3) {\AA}. It exhibits charge
density wave (CDW) order at room temperature with a modulation wave vector
$\mathbf{q}$ = 1/2$\mathbf{b}$* + 0.3478$\mathbf{c}$* originating from
electronic instability of Te-square nets in [LaTe$_{3}$] layers. The Mn analog
exhibits a cluster spin glass behavior with spin freezing temperature
$T_{\mathrm{f}}$ $\approx$ 5 K attributed to disordered Mn vacancies and
competing magnetic interactions in the [Mn$_{1-x}$Te] layers. The Zn analog
also has charge density wave order at room temperature with a similar
$\mathbf{q}$-vector having the $\mathbf{c}$* component ~ 0.346 confirmed by
selected-area electron diffraction (SAED). Electron transfer from
[K$M_{1-x}$Te] to [LaTe$_{3}$] layers exists in KLa$M_{1-x}$Te$_{4}$, leading
to an enhanced electronic specific heat coefficient. The resistivities of
KLa$M_{1-x}$Te$_{4}$ ($M$ = Mn, Zn) exhibit metallic behavior at high
temperatures and an upturn at low temperatures, suggesting partial localization
of carriers in the [LaTe$_{3}$] layers with some degree of disorder associated
with the $M$ atom vacancies in the [$M_{1-x}$Te] layers.
