Inversion Symmetry and Wave-Function-Nodal-Lines of Dirac Electrons in Organic Conductor alpha-(BEDT-TTF)_2I_3

By examining organic conductor alpha-(BEDT-TTF)_2I_3 which is described by a nearest neighbors tight-binding model it is shown that because of inversion symmetry, each component of a wave function (WF) exhibits nodal lines (NLs) in the Brillouin zone. In the absence of any band crossing, each NL connects two time reversal invariant momenta (TRIM) as partners. In the presence of a pair of Dirac points (band crossing), for each band that crosses and for each WF component there is a NL that connects the pair of Dirac points via a TRIM without partner. This second kind of NL leads to a discontinuous sign change for non vanishing components of the WF. Such a property is at the origin of the +/- pi Berry phase accumulated on a contour integral encircling one Dirac point. The results are examplified by numerical calculation of WFs components for the above conductor with a 3/4 filled band.