Effect of electron corelation on superconducting pairing symmetry

TL;DR

This paper investigates how electron correlations influence different superconducting pairing symmetries, revealing that correlations suppress s-wave gaps faster than d-wave, and affect complex order parameters and gap anisotropy.

Contribution

It provides a detailed analysis of the impact of electron correlation on s, d, and mixed s+id pairing symmetries using the slave boson formalism, highlighting novel effects on gap behavior and transition temperatures.

Findings

Electron correlation suppresses s-wave gap and $T_c$ faster than d-wave.

In mixed $s+id$ states, $d$-wave gap can increase with correlation while $T_c^d$ remains unchanged.

Gap anisotropy varies with electron correlation and is discussed in context of experiments.

Abstract

The role of electron correlation on different pairing symmetries are discussed in details where the electron correlation has been treated within the slave boson formalism. It is shown that for a pure $s$ or pure $d$ wave pairing symmetry, the electronic correlation suppresses the $s$ wave gap magnitude (as well as the $T_c$) at a faster rate than that for the $d$ wave gap. On the otherhand, a complex order parameter of the form ($s+id$) shows anomalous temperature dependence. For example, if the temperature ($T_{c}^d$) at which the $d$ wave component of the complex order parameter vanishes happens to be larger than that for the $s$ wave component ($T_{c}^s$) then the growth of the $d$ wave component is arrested with the onset of the $s$ wave component of the order parameter. In this mixed phase however, we find that the suppression in different components of the gap as well as the corresponding $T_c$ due to coulomb correlation are very sensitive to the relative pairing strengths of $s$ and $d$ channels as well as the underlying lattice. Interestingly enough, in such a scenario (for a case of $T_{c}^s > T_{c}^d$) the gap magnitude of the $d$ wave component increases with electron correlation but not $T_{c}^d$ for certain values of electron correlation. However, this never happens in case of the $s$ wave component. We also calculate the temperature dependence of the superconducting gap along both the high symmetry directions ($\Gamma$ - M and $\Gamma $ - X) in a mixed $s+id$ symmetry pairing state and the thermal variation of the gap anisotropy ($\frac{\Delta_{\Gamma - M}}{\Delta_{\Gamma - X}}$) with electron correlation. The results are discussed with reference to experimental observations.