Symmetry of superconducting states with two orbitals on a tetragonal lattice: application to $LaO_{1-x}F_{x}FeAs$

TL;DR

This paper classifies possible superconducting states in two-orbital tetragonal systems using group theory, highlighting how orbital symmetry influences pairing parity and discussing implications for iron-based superconductors.

Contribution

It provides a systematic group-theoretical classification of superconducting states with two orbitals on a tetragonal lattice, including effects of spin-orbit coupling and orbital symmetry.

Findings

Orbital symmetric states have even parity for spin singlet and odd for spin triplet.

Orbital anti-symmetric states have odd parity for spin singlet and even for spin triplet.

Anti-symmetric orbital states are stable only for degenerate orbitals in weak pairing limit.

Abstract

We use group theory to classify the superconducting states of systems with two orbitals on a tetragonal lattice. The orbital part of the superconducting gap function can be either symmetric or anti-symmetric. For the orbital symmetric state, the parity is even for spin singlet and odd for spin triplet; for the orbital anti-symmetric state, the parity is odd for spin singlet and even for spin triplet. The gap basis functions are obtained with the use of the group chain scheme by taking into account the spin-orbit coupling. In the weak pairing limit, the orbital anti-symmetric state is only stable for the degenerate orbitals. Possible application to iron-based superconductivity is discussed.