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

First-order electronic phase transition in $\alpha$-(BEDT-TTF)$_2$I$_3$ revealed by temperature-dependent generalized ellipsometry