Gap Symmetry and Stability Analysis in the Multi-Orbital Fe-Based Superconductors

TL;DR

This paper introduces a stability criterion for multi-orbital superconductors that helps identify the most stable pairing states and the minimal Hamiltonian needed to compare different instabilities.

Contribution

It provides a simple, energy-based criterion for analyzing the stability of orbital gap functions in multi-orbital superconductors, aiding in understanding pairing mechanisms.

Findings

A stability analysis criterion based on pairing electrons of equal energy.

Identification of Hamiltonian terms that suppress specific superconducting states.

Method to determine the minimal Hamiltonian for competing instabilities.

Abstract

The iron-based superconductors allow for a zoo of possible order parameters due to their orbital degrees of freedom. These order parameters are often written in an orbital basis, as this allows to distinguish their different symmetry. Unlike in standard single-band superconductors, where electrons of the same band - and hence, energy - are paired, a general order parameter in such a multi-orbital system also contains pairing of electrons belonging to different bands. As this corresponds to pairing of electrons of different energy, such order parameters are energetically less stable. Here, we present a simple criterion for a stability analysis of the orbital part of the gap function based on the basic principle that electrons of equal energy are paired in the superconducting state. This not only allows to find the most stable states, but also to identify the terms in a (tight-binding) Hamiltonian suppressing any given superconducting state. Our approach thus allows to identify the minimal Hamiltonian necessary to compare competing instabilities.