Enhanced electron-phonon coupling due to layered-perovskites octahedral tilting in hole doped cuprate superconductor

The electron-phonon (e-ph) coupling is crucial in explaining various ordering phenomena such as superconductivity and charge density waves (CDW) which has been invoked to explain Cooper pair formation leading to superconductivity, however, the origin of charge state mechanism is not yet fully understood. Here we study the role of e-ph coupling in understanding the interplay of the structural phase transition, CDW transition, superconducting transition, and flat electronic band dispersion in the La$_{2-x}$Sr$_{x}$CuO$_4$ ($x$ = 0.15) superconductor. We employed high-resolution temperature dependent x-ray diffraction and Raman scattering measurements in combination with first-principles calculations across the phase-transitions. We unveil the dominant role of CuO$_6$ octahedra distortion and tilting which suggests the presence of strong e-ph coupling that gradually develops high alternating CuO$_6$ octahedra rotations [in-phase (+ve) and anti-phase (-ve); $\phi$ $\approx$ 3$^{\circ}$)] which can further enhanced e-ph coupling below the structural-phase transition ($T_s$ = 150 K), leading to the symmetry-breaking. We observe that the local distortion of CuO$_6$ including tilting and phonon modes at $\cong$ 430, 360, 225, and 100 cm$^{-1}$ may associated with CDW correlations below $T_s$. Further, our theoretical calculations across the superconducting transition suggests the presence of strong hybridization of Cu 3$d$ with O 2$p$ orbitals, indicating the role of alternating CuO$_6$ octahedra tilt in the electronic structure of La$_{2-x}$Sr$_{x}$CuO$_4$. Thus, the octahedral tilt played a crucial role in the origin of the CDW phase.