Effect of the Vortices on the Nuclear Spin Relaxation Rate in the Unconventional Pairing States of the Organic Superconductor (TMTSF)$_2$PF$_6$

TL;DR

This paper theoretically investigates how vortices influence nuclear spin relaxation rates in the unconventional superconducting state of (TMTSF)$_2$PF$_6$, focusing on the effects of different pairing symmetries and vortex states.

Contribution

It introduces a theoretical framework to analyze vortex effects on spin relaxation in quasi-one-dimensional superconductors with various pairing symmetries.

Findings

T_1^{-1} is proportional to T at low temperatures with line nodes.

Vortices induce quasiparticles at the Fermi energy that relax spins.

The study aids in identifying the pairing symmetry of (TMTSF)_2PF_6.

Abstract

This Letter theoretically discusses quasiparticle states and nuclear spin relaxation rates $T_1^{-1}$ in a quasi-one-dimensional superconductor (TMTSF)$_2$PF$_6$ under a magnetic field applied parallel to the conduction chains. We study the effects of Josephson-type vortices on $T_1^{-1}$ by solving the Bogoliubov de Gennes equation for $p$-, $d$- or $f$-wave pairing interactions. In the presence of line nodes in pairing functions, $T_1^{-1}$ is proportional to $T$ in sufficiently low temperatures because quasiparticles induced by vortices at the Fermi energy relax spins. We also try to identify the pairing symmetry of (TMTSF)$_2$PF$_6$.