<i>Ab initio</i> phase diagram of PbSe crystals calculated with the random phase approximation

Understanding the phase behavior of semiconductor materials is important for applications in solid state physics and nanoscience. Accurate experimental data is often difficult to obtain due to strong kinetic effects. In this work, we calculate the temperature-pressure phase diagram of lead selenide (PbSe) using the random phase approximation (RPA), an accurate wave-function-based many-body technique. We consider three crystalline phases, the low pressure B1 phase (NaCl type), the intermediate B33 phase (CrB type), and the high pressure B2 phase (CsCl type). The electronic contributions to the free energy (at $T=0\phantom{\rule{0.16em}{0ex}}\text{K}$) are calculated in the Born-Oppenheimer approximation using the RPA, whereas phononic contributions are computed in the quasiharmonic approximation using density functional theory and the PBEsol functional. At room temperature, we find transition pressures of $4.6\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ for the B1 $\ensuremath{\leftrightarrow}$ B33 transition and $18.7\ifmmode\pm\else\textpm\fi{}0.3\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ for the B33 $\ensuremath{\leftrightarrow}$ B2 transition, in good agreement with experiments. In contrast to the interpretation of recent experiments, we observe a negative Clapeyron slope for both transitions. Gibbs free energy differences between competing structures have small gradients close to coexistence, consistent with pronounced hysteresis observed in experiments. The phase diagram presented in this work can serve as a reference for future studies of PbSe and should prove useful in the development of accurate and efficient force fields.