Evidence of Andreev bound states as a hallmark of the FFLO phase in κ-(BEDT-TTF)2Cu(NCS)2

Abstract

. This momentum leads to a spatially inhomogeneous state consisting of periodically alternating 'normal' and 'superconducting' regions. Here, we establish that the hallmark of this state is the appearance of spatially localized and spin-polarized quasiparticles forming the so-called Andreev bound states (ABS). These are detected through our nuclear magnetic resonance (NMR) measurements.The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is expected to occur in the vicinity of the upper critical magnetic field (H c2 ) when Pauli pair breaking dominates over orbital (vortex) effects [2][3][4][5] . Pauli pair breaking prevails in fields that exceed the Pauli limit (H p ) for which the Zeeman energy is strong enough to break the Cooper pair by flipping one spin of the singlet. Intense efforts have been invested to search for indisputable evidence for the existence of the FFLO states. Examples include a theoretical proposal for detecting modulated superfluid phases in optical lattices 6 ; tunnelling in superconducting (SC) films 7 ; mapping of the phase diagram of CeCoIn 5 (refs 8,9), and studies of layered organic superconductors [10][11][12][13] . However, clear microscopic evidence for an FFLO phase is still missing. In the FFLO state, in the vicinity of the transition from the SC to FFLO state, nodes in the order parameter form the domain walls, where the superconducting phase changes by π . This phase twist leads to a local modification of the electronic density of states (DOS) and the creation of new topological ABS (ref. 14), the observation of which we report here.Besides CeCoIn 5 , where a putative FFLO state coexists with long-range magnetism, the organic compound, κ-(BEDT-TTF) 2 Cu(NCS) 2 (hereafter referred to as κ-(ET) 2 X) exhibits the clearest thermodynamic evidence for the existence of a narrow intermediate SC phase 11 . Because this SC phase is stabilized in magnetic fields (H ) that exceed the Pauli limit, H p ≈ 20.7 T (ref. 15), as illustrated in Fig. 1, it has been identified as an FFLO phase. Recent measurements of NMR spectra gave evidence that the phase transition within the SC state is Zeeman-driven 16 , but failed to provide a clear hallmark of the FFLO state. Our main discovery is that the NMR spin-lattice relaxation rate (T significantly enhanced, as compared to its normal-state value, in the SC state for fields exceeding H p . We deduce that the enhancement stems from the ABS of polarized quasiparticles spatially localized in the nodes of the order parameter in an FFLO state. Furthermore, we reveal that these topological ABS are profoundly different from the sub-gap states found in vortex cores, as they are shifted in energy away from the Fermi level by an amount controlled by the magnetic field. We first examine the NMR spectral lineshapes in different regimes at 22 T, shown in the inset to Fig. 2, to demonstrate the sensitivity of our measurements to different superconducting phases in this compound. These 13 C NMR spectra reflect the distribution of the hyperfine fields and are thus a sen...

Spin susceptibility of Andreev bound states

“…This enhancement mostly appears due to transitions between Andreev bound states and the propagating continuum states that can occur in high fields, µ B H = 0.5∆, close to the Pauli limiting field in D-wave µ B H P = 0.55∆ 0 . The range of fields where it appears is in good agreement with experimental observations in κ-(BEDT-TTF) 2 Cu(NCS) 2 near the first-order superconducting-normal transition, 14 although we find the magnitude of the enhancement is somewhat smaller than the measured value.…”

Multiple phase transitions in Pauli-limited iron-based superconductors

“…CeCoIn 5 [7][8][9][10][11]) or organic superconductors (e.g. [14][15][16][17][18]). These chemical compounds are often modeled as effectively quasi-2D one-band systems.…”

Orbital effect for the Fulde-Ferrell-Larkin-Ovchinnikov phase in a quasi-two-dimensional superconductor in a parallel magnetic field

“…[27,28] is that the orbital effect is of the relative order of t 2 ⊥ /T 2 c0 1. From the experimental side, plenty of experimental works on Q2D organic and some other superconductors have been performed [29][30][31][32][33][34][35][36][37][38][39][40][41] to establish the possible existence of the FFLO phase in a parallel magnetic field.The goal of our paper is to consider the orbital effect in a parallel magnetic field in a Q2D conductor at zero temperature, in contrast to Refs. [27,28].…”