  Mesoscopic irregularly ordered and even amorphous self-assembled electronic
structures were recently reported in two-dimensional metallic dichalcogenides
(TMDs), created and manipulated with short light pulses or by charge injection.
Apart from promising new all-electronic memory devices, such states are of
great fundamental importance, since such aperiodic states cannot be described
in terms of conventional charge-density-wave (CDW) physics. In this paper we
address the problem of metastable mesoscopic configurational charge ordering in
TMDs with a sparsely filled charged lattice gas model in which electrons are
subject only to screened Coulomb repulsion. The model correctly predicts
commensurate CDW states corresponding to different TMDs at magic filling
fractions $f_m=1/3,1/4,1/9,1/13,1/16$. Doping away from $f_m$ results either in
multiple near-degenerate configurational states, or an amorphous state at the
correct density observed by scanning tunnelling microscopy. Quantum
fluctuations between degenerate states predict a quantum charge liquid at low
temperatures, revealing a new generalized viewpoint on both regular, irregular
and amorphous charge ordering in transition metal dichalcogenides.
