  We investigate the effect of strong electronic correlation on the massless
Dirac fermion system, $\alpha$-(BEDT-TTF)$_2$I$_3$, under pressure. In this
organic salt, one can control the electronic correlation by changing pressure
and access the quantum critical point between the massless Dirac fermion phase
and the charge ordering phase. We theoretically study the electronic structure
of this system by applying the slave-rotor theory and find that the Fermi
velocity decreases without creating a mass gap upon approaching the quantum
critical point from the massless Dirac fermion phase. We show that the
pressure-dependence of the Fermi velocity is in good quantitative agreement
with the results of the experiment where the Fermi velocity is determined by
the analysis of the Shubnikov-de Haas oscillations in the doped samples. Our
result implies that the massless Dirac fermion system exhibits a quantum phase
transition without creating a mass gap even in the presence of strong
electronic correlations.
