Continuum Lowering in a Solid under Extreme Pressure and Temperature: Fermi Surface Rising and Re-entrant Semimetallicity*

Continuum lowering is an important spectroscopic diagnostic of extreme conditions in experiments where the X-ray transition energies are usually reduced with increasing pressure and/or temperature in plasmas. The corresponding effects in solids under those extreme conditions have not been yet established. We perform density functional theory calculations on diamond-structure silicon as a representative solid, and compute the absorption onset of soft x-rays up to 17× compression (~340 Mbar) and high electronic temperatures. The potential shows continuum lowering like in plasmas but the absorption onset rises with pressure unlike for typical plasmas, because of Fermi surface rising and quantum degeneracy. Additionally, silicon becomes semimetallic and then metallic at low compressions, but then again semimetallic at high compressions, which is correlated with delocalization of the electrons out of the atoms.  We compare our results to common ionization models, verify our pseudopotential approximation, and validate the quality of the absorption spectra with GW/Bethe-Salpeter calculations. Our studies provide insight into the relative effects of pressure and temperature in continuum lowering of solids for design and interpretation of high energy density spectroscopy.