First-order polymorphic phase transition in supercooled liquid Silicon

We perform first-principles molecular dynamics simulation of liquid and supercooled liquid Silicon.~ Looking at the volume dependence of the pressure at different supercooled liquid temperatures, we find a van der-Waals loop, indicating a possible liquid-liquid first-order phase transition.~ It appears that the transition can be seen only at pressures of about a few GPa.~ We analyze our data using the zero'th moment of the tetrahedral order parameter, $q_i =1-\frac{3}{8}\sum\limits_{j>k} {[\cos \theta _{ijk} +\frac{1}{3}]^2} $[1], where $\theta _{ijk} $ is the angle formed between neighbors `$j$' and `$k$' and the central atom `$i$'. For a perfect tetrahedral arrangement ($\cos \theta _{ijk} =-\frac{1}{3})$ the value of the order-parameter is `1' and for an uncorrelated system its distribution is peaked at `0'. We find that the low temperature liquid has a more tetrahedral open network than the high temperature one, indicating that the transition is between a high-density and a low-density liquid. The electronic density of states along an isochore indicates a sharp drop in metallicity across the transition temperature, which we believe lies around T = 1100K. [1] M. Scott Shell and Pablo G. Debenedetti and Athanassios Z. Panagiotopoulos, Physical Review E \textbf{66}, 011201, (2002)