Finite-Temperature ab initio Structural Optimization of the Bilayer Nickelate Superconductor La₃Ni₂O₇

La₃Ni₂O₇ is a recently discovered high-temperature superconductor with a critical temperature of 80~K under high pressure [1]. The superconducting phase is accompanied by a structural phase transition involving symmetry breaking, making the understanding of temperature and pressure dependence of the crystal structure essential for elucidating the mechanisms of superconductivity in nickelate systems.



However, determining the precise symmetry of La₃Ni₂O₇ under extreme conditions—such as high pressure and low temperature—remains experimentally challenging. Consequently, a comprehensive and reliable temperature-pressure phase diagram has yet to be established.



In this study, we present the temperature-pressure phase diagram of La₃Ni₂O₇ constructed using first-principles calculations. For the phase diagram calculations, structural optimization within a finite temperature range was performed based on self-consistent phonon (SCP) theory [2]. This method has been reported to reproduce the structural phase transition in BaTiO₃ [3], and if it enables prediction of the crystal structure of this material, it is expected to provide guidance for material design in similar systems in the future.



Furthermore, due to the high computational cost associated with the large number of atoms in this material's structure optimization, we also worked on improving the optimization method. We implemented the GDIIS (Geometry optimization using Direct Inversion in the Iterative Subspace) method [4], which is expected to accelerate convergence. We also discuss the changes in computational time between the conventional Newton method search and the newly implemented method.

[1] H. Sun, et al. Nature 621, 493 (2023).

[2] T. Tadano, et al. Condens. Matter, 26, 225402 (2014).

[3] R. Masuki, et al. Phys. Rev. B, 106, 224104 (2022).

[4] Ö. Farkas and H. B. Schlegel, Phys. Chem. Chem. Phys, 4, 11-15 (2002).