Pairing Symmetry, Nodal and Antinodal Superconducting Gap in ${\text{La}}_{2-x}{\text{Sr}}_x{\text{CuO}}_4$: A Doping Scenario

Using the many-body quantum dynamics and Dyson's equation formalism, the phonon Green's function has been developed via a Hamiltonian that includes the contribution of harmonic electron and phonon field and their interaction, phonon field anharmonicities and defects. The renormalized electron–phonon dispersion is obtained using the modified form of Born–Mayer–Huggins potential (MBMHP) and phonon Green's function for a representative high-temperature superconductor (HTS) ${\text{La}}_{2-x}{\text{Sr}}_x{\text{CuO}}_4$. The in-plane gap analysis has produced a v-shaped gap that confesses the anisotropy of the superconducting gap (SG). The nodal gap, antinodal gap and SG exhibit increment with decreasing doping with the vanishing of the nodal gap at $x=0.104$. A dominated $d_{x^2-y^2}$ pairing symmetry is observed along with a small component of s or $d_{xy}$ pairing state in the underdoped regime. The variation in the nodal gap, antinodal gap and SG shows monotonic increment with decreasing doping. It is found that doping has a nonlinear effect on $d_{x^2-y^2}$ pairing symmetry. The impact of antiferromagnetic (AF) spin fluctuations has been incorporated in the SG equation and on the pairing symmetry.