Hidden competing phase revealed by first-principles calculations of phonon instability in the nearly optimally doped cuprate La_1.875Sr_0.125CuO₄

The representative cuprate La2-xMxCuO4 with M = 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 La2-xSrxCuO4, is found to be the ground state where the structural phase transitions HTT -> LTO -> LTLO can be understood via phonon instability. Although the La-O composition is identified to be responsible for the phonon softening, the superconducting CuO2 layer is dynamically stable. The LTLO phase, which can exhibit an similar to 20-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 La1.875Sr0.125CuO4 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 La2-xSrxCuO4.