Among the various many-body approaches employed in this area of research, it is becoming increasingly transparent that the strong e -e interaction regime in fewelectron nanosystems can be best described theoretically through the use of the microscopic full conguration interaction (FCI) methodology , which treats in a most ecient way the two-body part of the Hamiltonian governing the system. Indeed, the FCI (referred to also as exact diagonalization) has been successfully applied in the last two decades to twodimensional (2D) quantum dots (QDs) with single-band semiconductor materials substrates, like GaAs. FCI calculations for condensed-matter nanostructures that incorporate aspects of the VDOF have been also considered recently . However, a CI approach that unequivocally relates to the eld of valleytronics [3741] by properly incorporating the valley degree of freedom as an isospin , in complete analogy with the regular spin, is still missing.