# Robust d-wave pairing symmetry in multi-orbital cobalt high temperature superconductors

## TL;DR

This study demonstrates that multi-orbital cobalt high-temperature superconductors favor a robust d-wave pairing symmetry, with strong orbital selectivity, as shown by multiple theoretical approaches, indicating potential for experimental validation of high-$T_c$ mechanisms.

## Contribution

The paper provides the first comprehensive theoretical analysis showing robust d-wave pairing and orbital selectivity in cobalt high-$T_c$ superconductors using mean field, RPA, and FRG methods.

## Key findings

- d_{x^2-y^2} pairing symmetry is favored near half filling
- Superconductivity is strongly orbital selective, dominated by the d_{x^2-y^2} orbital
- Results suggest new materials can test high-$T_c$ pairing mechanisms

## Abstract

The pairing symmetry of the newly proposed cobalt high temperature (high-$T_c$) superconductors formed by vertex shared cation-anion tetrahedral complexes is studied by the methods of mean field, random phase approximation (RPA) and functional renormalization group (FRG) analysis. The results of all these methods show that the $d_{x^2-y^2}$ pairing symmetry is robustly favored near half filling. The RPA and FRG methods, which are valid in weak interaction regions, predict that the superconducting state is also strongly orbital selective, namely the $d_{x^2-y^2}$ orbital that has the largest density near half filling among the three $t_{2g}$ orbitals dominates superconducting pairing. These results suggest that the new materials, if synthesized, can provide indisputable test to high-$T_c$ pairing mechanism and the validity of different theoretical methods.