BAND-STRUCTURE METHODS FOR INCOMMENSURABLY MODULATED CRYSTALS - APPLICATION TO THE LOW-TEMPERATURE PHASE OF TETRATHIAFULVALENE-TETRACYANOQUINODIMETHANE (TTF-TCNQ)

The superspace description of incommensurably modulated crystals is used to generalize commonly used band-structure methods to cover this class of crystals. The methods considered are the nearly-free-electron method, the tight-binding method, and the Korringa-Kohn-Rostoker equations in the atomic-sphere approximation. Formulas describing the electrostatic potential and energies of an incommensurately modulated crystal are also given. This methodology is used to calculate the gap in the electronic spectrum of modulated phase of the organic conductor [2-(1,3-dithiole-2-ylidene)-1,3-dithiole]- {2,2'-(2,5-cyclohexadiene-1,4-diylidene)bis[propanedinitrile]} or tetrathiafulvalene-tetracyanoquinodimethane (TTF-TCNQ) from low-temperature x-ray-diffraction data. The calculation is based on a band-structure calculation for the isolated stacks of TTF molecules and TCNQ molecules using the valence-effective-Hamiltonian method. As a result, band gaps of 7 and 5 meV are found for the TCNQ and TTF stacks.