ON THE PHYSICAL AND STRUCTURAL CRITERIA OF THE EXISTENCE OF CRYSTAL SUPERLATTICES

Superlattices are characterized by diffraction patterns consisting of maxima with alternating intensities (the so-called miniband spectrum). The observation of such a miniband spectrum can be regarded as a phys ical criterion of the existence of a superlattice. A characteristic st ructural feature of superlattices is pseudosymmetry, due to which a co nsiderable part of the electron density is invariant with respect to t he operations of a certain translation supergroup of the space group o f the crystal. We introduce a quantitative measure of the translationa l pseudosymmetry eta(t)[rho(x)] and define the quantity eta above whi ch all the structures having translation symmetry would be characteriz ed by a miniband spectra and, hence, would be superlattices (the struc tural criterion of the existence of a superlattice). The criterion of the existence of a superlattice is established for natural crystals of the same structure type and for the one-dimensional Kronig-Penney mod el.