Spin susceptibility of Andreev bound states

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)$_2$.