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A zero-gap state (ZGS) has been found in a bulk system of two-dimensionalorganic conductor, $\alpha$-(BEDT-TTF)$_2$I$_3$ salt which consists of foursites of donor molecules in a unit cell. In the present paper, thecharacteristic of the ZGS is analyzed in detail and the electronic propertiesare examined in the vicinity of the contact point where the conduction andvalence bands degenerate to form the zero-gap. The eigenvectors of the energyband have four components of respective sites, where two of them correspond toinequivalent sites and the other two correspond to equivalent sites. It isshown that the former exhibits an exotic momentum dependence around the contactpoint and the latter shows almost a constant dependence. The density of statesof each site close to the Fermi point is calculated to demonstrate thetemperature dependence of the local magnetic susceptibility and the localnuclear magnetic relaxation rate. Further, the robust property of the ZGSagainst the anion potential is also shown by using the second-orderperturbation.

Electronic Properties Close to Dirac Cone in Two-Dimensional Organic Conductor $\alpha$-(BEDT-TTF)$_2$I$_3$