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 q vectors. Beside the dominant peak at ferromagnetic vector q = 0, we find significant enhancement of antiferromagnetic correlations at vectors q < ∼ 2k f , with 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 κ-(BEDT-TTF)2Cu(NCS)2.

Evidence for the Presence of the Fulde-Ferrell-Larkin-Ovchinnikov State in CeCu2Si2 Revealed Using Kitagawa1, Nakamine2, Ishida3 et al. 2018Phys. Rev. Lett.453190View full textAdd to dashboardCite

“…Mayaffre et al recently performed high-field nuclear magnetic resonance (NMR) measurements for a magnetic field parallel to the conducting plane, in κ-(BEDT-TTF) 2 Cu(NCS) 2 , which is one of the candidates for realizing the FFLO state, and they found a clear enhancement of the nuclear spin-lattice relaxation rate 1/T 1 in the field range between the Pauli-limiting field H P and H c2 (T ) [9], indicated by the appearance of the sharp bound states located away from E F . The enhancement of 1/T 1 suggested the formation of FFLO state, and it is in good agreement with the 1/T 1 calculation [10]. Therefore, taking 1/T 1 measurements around H c2 is recognized as a valuable method for searching the FFLO state.…”

“…First, the normalized increase of 1/T 1 T , (1/T 1 T ) peak /(1/T 1 T ) normal , differs. Although 1/T 1 T increased almost twofold in the case of κ-(BEDT-TTF) 2 Cu(NCS) 2 , in the present case (1/T 1 T ) peak /(1/T 1 T ) normal estimated from the magnetic field dependence of 1/T 1 T is ∼ 1.2 for H c and ∼ 1.3 for H ⊥ c. The increase in ratio of 1/T 1 T depends on the SC gap symmetry and the details of the Fermi surfaces of the systems [10]. Second, the enhancement of 1/T 1 T was observed for H c and H ⊥ c in CeCu 2 Si 2 while this enhancement was only observed for H conducting plane in the case of κ-(BEDT-TTF) 2 Cu(NCS) 2 .…”

Nuclear magnetic resonance in high magnetic field: Application to condensed matter physics

“…Recently, a high-field NMR experiment [30] has shown that these spin-polarized ABS produce a huge enhancement of the NMR relaxation rate 1/T 1 (Fig 6a), providing the first microscopic characterisation of an FFLO phase. It turns out that this effect only occurs in a limited range of relatively high temperature, which has been consistently explained by theory [181], showing that this enhancement comes from the scattering of electronic spins between the bound and continuum states. A new compound with much smaller H c2 values, β"-(BEDT-TTF) 2 SF 5 CH 2 CF 2 SO 3 , has been recently investigated [182] by NMR, confirming the nuclear spin-lattice relaxation results obtained in [30] are ubiquitous of the FFLO phase, and observing a lineshape compatible with a single-q modulated superconducting phase.…”

“…At 27 T, the system remains normal down to the lowest temperature investigated (1.4 K), while at 22 T, the system enters from the normal state into the FFLO phase. The huge peak in (T1T ) −1 is due to the Andreev bound states present in the FFLO phase [30,180,181]. Inset: Simulation of the (T1T ) −1 peak due to the Andreev bound states.…”

Spatially Inhomogeneous Superconducting State near Hc2 in UPd2Al3

“…However, it is noted that a strong enhancement in 1/T 1 T just below H c2 (T ), which is regarded as a hallmark of the FFLO state in κ−(BEDT-TTF) 2 Cu(NCS) 2 , 17) was not observed for UPd 2 Al 3 . It was shown from a theoretical study 18) that the enhancement in 1/T 1 T originates from the presence of the Andreev bound state inside the SC gap, and that the magnitude of the enhancement depends on the SC gap structure. Therefore, we consider that the different behavior of 1/T 1 T could be interpreted with the difference in SC gap structures of κ−(BEDT-TTF) 2 Cu(NCS) 2 and UPd 2 Al 3 .…”