Requirements for Zero-Gap States in Organic Conductors

Existence of zero-gap state in organic conductors is investigated within the framework of the tight-binding approximation. The zero-gap state is realized when the transfer integrals fulfill two conditions; one is the contact condition in which two energy bands have a contact point, and the second is the zero-gap condition where the Fermi level actually comes to the contact point. When a unit cell contains two molecules, a contact point appears if the dimerization gap along the main chain is smaller than the gap in the transverse direction. This condition is fulfilled by only a limited number of materials. A uniform square lattice with transverse transfers alternately with opposite signs is a simple system that has a zero-gap state. Numerical calculation indicates that most four-molecule materials have a contact point, but usually lead to electron and hole pockets. In alpha-(BEDT-TTF)(2)I-3 [BEDT-TTF: bis(ethylenedithio)tetrathiafulvalene], non-stripe charge order, particularly the existence of one charge-poor molecule, assists in realizing the actual zero-gap state. In this case, the presence of a molecule located on an inversion center is another requisite, because otherwise the non-stripe charge order destroys the inversion symmetry, and opens an energy gap.