Spin susceptibility of Andreev bound states

TL;DR

This paper calculates the spin susceptibility and relaxation rates near inhomogeneities in superconductors, revealing enhanced magnetic correlations linked to Andreev bound states, with implications for experimental detection.

Contribution

It provides a detailed theoretical analysis of spin responses in inhomogeneous superconductors, highlighting the role of Andreev bound states and their experimental signatures.

Findings

Enhanced spin susceptibility at certain wave vectors due to Andreev bound states.

Significant increase in spin-lattice relaxation rate at domain walls.

Suppression of features under moderate Zeeman fields.

Abstract

We calcuate electronic spin susceptibility and spin-lattice relaxation rate in singlet superconductor near a pairbreaking surface, or in a domain wall of the order parameter. We directly link presence of high-density Andreev bound states in the inhomogeneous region, combined with coherence factors, to enhancement of the susceptibility above the normal state's value for certain $\bf q$ vectors. Beside the dominant peak at ferromagnetic vector $q=0$, we find significant enhancement of antiferromagnetic correlations at vectors $q\lesssim 2 k_f$, with $\bf q$ $along$ the domain wall in $S$-wave superconductor, and $across$ domain wall in $D$-wave (nodes along the wall). These features are destroyed by applying moderate Zeeman field that splits the zero-energy peak. We solve Bogoliubov-de Gennes equations in momentum space and our results deviate from the lattice models investigated previously. Large enhancement of the spin-lattice relaxation rate $T_1^{-1}$ at the domain wall provides clear signature of the quasiparticle bound states, and is in good agreement with recent experiment in organic superconductor $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$.