Prediction of an unusual trigonal phase of superconducting LaH 10 stable at high pressures

Based on evolutionary crystal structure searches in combination with ab initio calculations, we predict an unusual structural phase of the superconducting ${\mathrm{LaH}}_{10}$ that is stable from about 250 to 425 GPa pressure. However, inclusion of phonon zero-point and 300 K free-energy contributions shifts the transition pressures to higher values. This phase belongs to a trigonal $R\overline{3}m$ crystal lattice with an atypical cell angle, ${\ensuremath{\alpha}}_{\mathrm{rhom}}\phantom{\rule{4pt}{0ex}}\ensuremath{\sim}\phantom{\rule{4pt}{0ex}}24.{56}^{\ensuremath{\circ}}$. We find that this structure contains three units of ${\mathrm{LaH}}_{10}$ in its primitive cell, unlike the previously known trigonal phase, in which the primitive cell contains only one ${\mathrm{LaH}}_{10}$ unit. In this phase, a 32-H-atom cage encapsulates La atoms, analogous to the lower-pressure fcc phase. However, the hydrogen cages of the trigonal phase consist of quadrilaterals and hexagons, in contrast to the cubic phase, which exhibits squares and regular hexagons. Surprisingly, the shortest H-H distance in this phase is shorter than that of the lower-pressure cubic phase and of atomic hydrogen metal. We find a structural phase transition from trigonal to hexagonal at 492 GPa at 300 K, where the hexagonal crystal lattice coincides with earlier predictions. Solving the anisotropic Migdal-Eliashberg equations, we find that the predicted trigonal phase (for standard values of the Coulomb pseudopotential) is expected to become superconducting at a critical temperature of about 175 K, which is less than ${T}_{c}\ensuremath{\sim}250$ K measured for cubic ${\mathrm{LaH}}_{10}$.