The dynamics of a single electron is considered on a periodic square lattice constructed
of rhomboidal quantum wells interacting via narrow links. The spectral structure
of bands and gaps of the lattice is derived from an accurate analysis of Bloch waves, based
on DN- maps of the quantum wells. For periodic lattice with rhomboidal periods, a solvable
model, is constructed based on a rational approximation of DN- maps of the quantum
wells by establishing a communication between them via partial boundary conditions emulating
the covalent bonds. In the case of the corresponding double periodic lattice, the weak
interaction of the two parallel periodic quasi-2d sub-lattices defines, due to the 2d Landau-
Zener effect, a high mobility of the corresponding charge carriers in certain direction on the
quasi-momenta plane.
