  The nature of correlation-driven metal-insulator transitions remains a
longstanding puzzle in solid-state physics. While some theories suggest a
second-order character, various experimental observations in these materials
indicate first-order phase transitions. Despite considerable progress over the
last decades in understanding the underlying driving mechanisms of
metal-insulator transitions, in particular the phase coexistence remains poorly
understood on a microscopic scale. Here, we employ Mueller matrix spectroscopic
and temperature-dependent ellipsometry to determine the anisotropic dielectric
functions of the two-dimensional charge-transfer salt
$\alpha$-(BEDT-TTF)$_2$I$_3$ across its charge-order metal-insulator
transition. Our results offer valuable insights into temperature-dependent
changes of the dielectric functions along the different crystallographic axes.
Furthermore, we apply an effective-medium approximation to quantify the
correlation between the metal-to-insulator transition and the volume fraction
of the metallic phase embedded within the insulating phase. Through this
comprehensive approach, generalized ellipsometry unravels the nature of the
correlation-driven metal-insulator transition.
