Three-Dimensional Topological Semimetal/Insulator States in \alpha-Type Organic Conductors with Interlayer Spin-Orbit Interaction

We have studied the tight-binding model for the \alpha-type layered organic conductors, \alpha-(ET)2I3 and \alpha-(BETS)2I3, with a uniform interlayer coupling accompanied by spin-orbit interaction originating from the I3- anion potential. The model preserves the time reversal and inversion symmetries. In \alpha-(ET)2I3, the interlayer spin-orbit coupling realizes the experimentally suggested Dirac semimetal state with inversion symmetry. In contrast, the inversion breaking in interlayer hoppings realizes the Weyl semimetal state without spin-orbit coupling. In \alpha-(BETS)2I3, the proposed strong topological insulator is hardly realized with inversion symmetry.