  ABSTRACT: Narrow-gap semiconductors are sought-after materials due to their
potential for long-wavelength detectors, thermoelectrics, and more recently
non-trivial topology. Here we report the synthesis and characterization of a
new family of narrow-gap semiconductors, $R$$_{3}$Cd$_{2}$As$_{6}$ ($R=$ La,
Ce). Single crystal x-ray diffraction at room temperature reveals that the As
square nets distort and Cd vacancies order in a monoclinic superstructure. A
putative charge-density ordered state sets in at 279~K in
La$_{3}$Cd$_{2}$As$_{6}$ and at 136~K in Ce$_{3}$Cd$_{2}$As$_{6}$ and is
accompanied by a substantial increase in the electrical resistivity in both
compounds. The resistivity of the La member increases by thirteen orders of
magnitude on cooling, which points to a remarkably clean semiconducting ground
state. Our results suggest that light square net materials within a $I4/mmm$
parent structure are promising clean narrow-gap semiconductors.
