# Orbital Symmetry and Orbital Excitations in High-$T_c$ Superconductors

## TL;DR

This paper explores how multiple orbital symmetries may contribute to high-temperature superconductivity, discussing models, experimental evidence, and potential mechanisms involving $x^2-y^2$, $e_g$, and $t_{2g}$ orbitals across various materials.

## Contribution

It introduces a comprehensive discussion on the role of multiple orbital symmetries in high-$T_c$ superconductors, highlighting new pathways and models for orbital contributions.

## Key findings

- Orbital excitations suggest a simplified single $x^2-y^2$ orbital model.
- Multiple orbital symmetries can contribute to superconductivity in various materials.
- Orbital-selective pairing and nematicity are observed in Fe-based superconductors.

## Abstract

We discuss a few possibilities of high-$T_c$ superconductivity with more than one orbital symmetry contributing to the pairing. First, we show that the high energies of orbital excitations in various cuprates suggest a simplified model with a single orbital of $x^2-y^2$ symmetry doped by holes. Next, several routes towards involving both $e_g$ orbital symmetries for doped holes are discussed: (i) some give superconductivity in a CuO$_2$ monolayer on Bi2212 superconductors, Sr$_2$CuO$_{4-\delta}$, Ba$_2$CuO$_{4-\delta}$, while (ii) others as nickelate heterostructures or Eu$_{2-x}$Sr$_x$NiO$_4$, could in principle realize it as well. At low electron filling of Ru ions, spin-orbital entangled states of $t_{2g}$ symmetry contribute in Sr$_2$RuO$_4$. Finally, electrons with both $t_{2g}$ and $e_g$ orbital symmetries contribute to the superconducting properties and nematicity of Fe-based superconductors, pnictides or FeSe. Some of them provide examples of orbital-selective Cooper pairing.