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Liquid-liquid phase transition in deeply supercooled Stillinger-Weber silicon

The existence of a phase transition between two distinct liquid phases in single-component network-forming liquids (e.g., water, silica, silicon) has elicited considerable scientific interest. The challenge, both for experiments and simulations, is that the liquid-liquid phase transition occurs under deeply supercooled conditions, where crystallization occurs very rapidly. Thus, early evidence from numerical equation of state studies was challenged, with the argument that slow spontaneous crystallization had been misinterpreted as evidence of a second liquid state. Rigorous free energy calculations have subsequently confirmed the existence of a liquid-liquid phase transition in some models of water, and exciting new experimental evidence has since supported these computational results. Similar results have so far not been found for silicon. Here, we present results from free energy calculations performed for silicon modelled with the classical, empirical Stillinger-Weber potential. Through a careful study employing state-of-the-art constrained simulation protocols and numerous checks for thermodynamic consistency, we find that there are two distinct metastable liquid states and a phase transition. Our results resolve a long-standing debate concerning the existence of a liquid-liquid transition in supercooled liquid silicon and address key questions regarding the nature of the phase transition and the associated critical point.