Odd-frequency Cooper pairs in two-band superconductors and their magnetic response

TL;DR

This paper analytically explores the emergence of odd-frequency Cooper pairs in two-band superconductors, revealing their paramagnetic response and implications for superconducting stability, especially in materials like MgB₂ and iron pnictides.

Contribution

It demonstrates how band hybridization and asymmetry induce odd-frequency pairs in two-band superconductors and analyzes their magnetic response and stability implications.

Findings

Odd-frequency pairs exhibit paramagnetic behavior.

Band hybridization induces odd-frequency pairing.

Odd-frequency pairing affects superconducting stability.

Abstract

We discuss odd-frequency Cooper pairs appearing in two-band superconductors by solving the Gor'kov equation analytically. We introduce the equal-time $s$-wave pair potentials as realized in MgB$_2$ and iron pnictides. Although the order parameter symmetry is conventional, the band degree of freedom enriches the symmetry variety of pairing correlations. The hybridization and the asymmetry between the two conduction bands induce odd-frequency pairs as a subdominant pairing correlation in the uniform ground state. To study the magnetic response of odd-frequency Cooper pairs, we analyze the Meissner kernel represented by the Gor'kov Green function. In contrast to the even-frequency pairs linked to the pair potential, the induced odd-frequency Cooper pairs indicate a paramagnetic property. We also discuss the relation between the amplitude of the odd-frequency pairing correlation and the stability of superconducting states in terms of the self-consistent equation for the pair potential.