  The charge-ordered insulator $\alpha$-(BEDT-TTF)$_2$I$_3$ gradually evolves
to a metal when pressure is applied, and at low temperatures the electronic
bands form tilted Dirac-like cones. A metallic state with a
frequency-independent optical conductivity indicates the coexistence of the
trivial and massless Dirac electrons in the system. Our infrared investigations
also reveal that at the boundary between insulating and metallic states an
energy gap opens due to correlated massive Dirac fermions, which is gradually
suppressed when pressure increases.
