We report on the Shubnikov de Haas (SdH) oscillations in the quasi two-dimensional molecular conductor $alpha-$(BETS)$_{2}$I$_{3}$ [BETS: bis(ethylenedithio)tetraselenafulvalene] laminated on polyimide films at 1.7 K. From the SdH phase factor, we verified experimentally that the material is in the Dirac fermion phase under pressure. $alpha-$(BETS)$_{2}$I$_{3}$ is in the vicinity of the phase transition between strongly correlated insulating and Dirac fermion phases, and is a possible candidate for an ambient-pressure molecular Dirac fermion system. However, the SdH oscillations indicate that the Berry phase is zero at ambient pressure. Under pressure, a $pi$ Berry phase emerges when the metal-insulator crossover is almost suppressed at $sim$0.5 GPa. The results contrast those for the pioneering molecular Dirac fermion system $alpha-$(BEDT-TTF)$_{2}$I$_{3}$ [BEDT-TTF: bis(ethylenedithio)tetrathiafulvalene] in which Dirac fermions and semiconducting behavior are simultaneously observed.
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