The representative cuprate ${\mathrm{La}}_{2-x}{M}_x{\mathrm{CuO}}_4$ with $M=\mathrm{Sr}$ and $x=1/8$ is studied via first-principles calculations in the high-temperature tetragonal (HTT), low-temperature orthorhombic (LTO), and low-temperature less-orthorhombic (LTLO) structures. By suppressing the magnetism and superconductivity, the LTLO phase, which has rarely been observed in ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, is found to be the ground state where the structural phase transitions $\mathrm{HTT}\to \mathrm{LTO}\to \mathrm{LTLO}$ can be understood via phonon instability. Although the La-O composition is identified to be responsible for the phonon softening, the superconducting ${\mathrm{CuO}}_2$ layer is dynamically stable. The LTLO phase, which can exhibit an $\sim 20\text{−}\mathrm{meV}$ splitting in the density of states, is proposed to have an intimate relationship with the observed pseudogap and the charge-density wave giving the stripe. We argue that at low temperatures, the superconducting LTO ${\mathrm{La}}_{1.875}{\mathrm{Sr}}_{0.125}{\mathrm{CuO}}_4$ competes with the phonon-preferred LTLO phase by spontaneously forming the Cooper pairs, resulting in suppressing the stripe. Therefore, the revealed LTLO phase is indispensable for understanding ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$.

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• Dynamical phase transitions
• Electronic structure
• Impurities in superconductors
• Lattice dynamics
• Phonons
• Structural phase transition
• Superconducting phase transition
• Cuprates
• High-temperature superconductors
• Density functional calculations
• Methods in superconductivity