LAUSR

We control the thickness of GaSe on the level of individual layers and study the corresponding optical absorption via highly sensitive differential transmission measurements. Suppression of excitonic transitions is observed when the number of layers is smaller than a critical value of 8. Through ab-initio modelling we are able to link this behavior to a fundamental change in the band structure that leads to the formation of a valence band shaped as an inverted Mexican hat in thin GaSe. The thickness-controlled modulation of the optical properties provides attractive resources for the development of functional optoelectronic devices based on a single material.