Magnetic and phonon mechanisms of superconductivity in La$_{2-x}$Sr$_x$CuO$_4$ support each other

TL;DR

This paper investigates how magnetic interactions and phonons jointly contribute to high-temperature superconductivity in La$_{2-x}$Sr$_x$CuO$_4$, showing they are comparable and reinforce each other.

Contribution

It provides a combined magnetic and phonon mechanism model for superconductivity with parameters calculated ab initio, highlighting their cooperative effects.

Findings

Magnetic and phonon contributions to T_c are of similar magnitude.

The model fits isotope effect data to determine the electron-phonon coupling parameter.

Magnetic and phonon mechanisms support each other in enhancing superconductivity.

Abstract

Strong electron correlations are responsible both for the insulator ground state of undoped La$_2$CuO$_4$ and strong antiferromagnetic coupling $J$ between neighbouring spins. We consider magnetic mechanism of superconducting pairing in the effective low energy $t - t' - t" - J^*$ model with all parameters calculated {\it ab initio}. Interaction of strongly correlated electrons with different phonon modes is also incorporated. In a BCS type theory the $d_{x^2 - y^2}$ gap is given by a sum of magnetic and phonon contributions. The phonon coupling parameter $\lambda = f(x)G$, where $G$ is a combination of bare electron-phonon couplings for all modes and the function $f$ depends on the hole concentration $x$ due to strong electron correlations. The main contribution to the only fitting parameter $G$ is determined by a competition of the breathing and buckling modes. Fitting the parameter $G$ from the isotope effect we obtain that magnetic and phonon contributions to the critical temperature $T_c $ work together and are of the same order of magnitude.