Probing and manipulating the Mexican hat-shaped valence band of In₂Se₃

Ferroelectrics based on van der Waals semiconductors represent an emergent class of materials for disruptive technologies ranging from neuromorphic computing to low-power electronics. However, many theoretical predictions of their electronic properties have yet to be confirmed experimentally and exploited. Here, we use nanoscale angle-resolved photoemission electron spectroscopy and optical transmission in high magnetic fields to reveal the electronic band structure of the van der Waals ferroelectric indium selenide (α-In₂Se₃). This indirect bandgap semiconductor features a weakly dispersed valence band, which is shaped like an inverted Mexican hat. Its form changes following an irreversible structural phase transition of α-In₂Se₃ into β-In₂Se₃ via a thermal annealing in ultra-high vacuum. Density functional theory supports the experiments and reveals the critical contribution of spin orbit coupling to the form of the valence band. The measured band structure and its in situ manipulation offer opportunities for precise engineering of ferroelectrics and their functional properties beyond traditional semiconducting systems.