Odd-frequency pairing and Kerr effect in the heavy-fermion superconductor UPt$_3$

TL;DR

This paper investigates how odd-frequency pairing naturally occurs in UPt$_3$ due to its crystal symmetry, spin-orbit coupling, and chiral order, linking it to observable Kerr rotation effects.

Contribution

It demonstrates the general emergence of odd-frequency pairing in UPt$_3$ and its connection to the Kerr effect, considering the effects of symmetry, spin-orbit coupling, and phase differences.

Findings

Odd-frequency pairing arises with inter-sublattice hopping or spin-orbit coupling.

Chiral order in the B phase induces additional odd-frequency amplitudes.

Finite Kerr rotation in the B phase correlates with the presence of odd-frequency pairing.

Abstract

We study the emergence of odd-frequency superconducting pairing in UPt$_3$. Starting from a tight-binding model accounting for the nonsymmorphic crystal symmetry of UPt$_3$ and assuming an order parameter in the $E_{2u}$ representation, we demonstrate that odd-frequency pairing arises very generally, as soon as inter-sublattice hopping or spin-orbit coupling is present. We also show that in the low temperature superconducting $B$ phase, the presence of a chiral order parameter together with spin-orbit coupling, leads to additional odd-frequency pair amplitudes not present in the $A$ or $C$ phases. Furthermore, we show that a finite Kerr rotation in the $B$ phase is only present if odd-$\omega$ pairing also exists.