Coherent interlayer coupling in quasi-two-dimensional Dirac fermions in $\alpha$-(BEDT-TTF)$_2$I$_3$

Theoretical and experimental studies have supported that the electronic structure of $\alpha$-(BEDT-TTF)$_2$I$_3$ under pressure is described by two-dimensional Dirac fermions. When the interlayer tunneling is coherent, the electronic structure of the system becomes three-dimensional, and we expect the peak structure to appear in the interlayer resistivity under magnetic fields. We theoretically and experimentally show that the peak appears in the interlayer resistivity at low temperatures and high magnetic fields. From the experiment, we estimate that the magnitude of the interlayer tunneling is $t_1 \sim 1$ meV. Our result opens the door to investigating the three-dimensional electronic structure of $\alpha$-(BEDT-TTF)$_2$I$_3$.