Progress made in the growth of “free-standing” (e.g., colloidal) quantum dots (see also articles in this issue by Nozik and Mićić, and by Alivisatos) and in the growth of semiconductor-embedded (“self-assembled”) dots (see also the article by Bimberg, Grundmann, and Ledentsov in this issue) has opened the door to new and exciting spectroscopic studies of quantum structures. These have revealed rich and sometimes unexpected features such as quantum-dot shape-dependent transitions, size-dependent (red) shifts between absorption and emission, emission from high excited levels, surface-mediated transitions, exchange splitting, strain-induced splitting, and Coulomb-blockade transitions. These new observations have created the need for developing appropriate theoretical tools capable of analyzing the electronic structure of 103–106-atom objects. The main challenge is to understand (a) the way the one-electron levels of the dot reflect quantum size, quantum shape, interfacial strain, and surface effects and (b) the nature of “many-particle” interactions such as electron-hole exchange (underlying the “red shift”), electron-hole Coulomb effects (underlying excitonic transitions), and electron-electron Coulomb (underlying Coulomb-blockade effects).
Interestingly, while the electronic structure theory of periodic solids has been characterized since its inception by a diversity of approaches (all-electron versus pseudopotentials; Hartree Fock versus density-functional; computational schemes creating a rich “alphabetic soup,” such as APW, LAPW, LMTO, KKR, OPW, LCAO, LCGO, plane waves, ASW, etc.), the theory of quantum nano-structures has been dominated mainly by a single approach so widely used that I refer to it as the “Standard Model”: the effective-mass approximation (EMA) and its extension to the “k · p” (where k is the wave vector and p is the momemtum). In fact, speakers at nanostructure conferences often refer to it as “theory” without having to specify what is being done. The audience knows.