. 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...

Puzzling aspects of high-transition-temperature (high-Tc) superconductors include the prevalence of magnetism in the normal state and the persistence of superconductivity in high magnetic fields. Superconductivity and magnetism generally are thought to be incompatible, based on what is known about conventional superconductors. Recent results, however, indicate that antiferromagnetism can appear in the superconducting state of a high-Tc superconductor in the presence of an applied magnetic field. Magnetic fields penetrate a superconductor in the form of quantized flux lines, each of which represents a vortex of supercurrents. Superconductivity is suppressed in the core of the vortex and it has been suggested that antiferromagnetism might develop there. Here we report the results of a high-field nuclear-magnetic-resonance (NMR) imaging experiment in which we spatially resolve the electronic structure of near-optimally doped YBa2Cu3O7-delta inside and outside vortex cores. Outside the cores, we find strong antiferromagnetic fluctuations, whereas inside we detect electronic states that are rather different from those found in conventional superconductors.

Study of the combined effects of strong electronic correlations with spin-orbit coupling (SOC) represents a central issue in quantum materials research. Predicting emergent properties represents a huge theoretical problem since the presence of SOC implies that the spin is not a good quantum number. Existing theories propose the emergence of a multitude of exotic quantum phases, distinguishable by either local point symmetry breaking or local spin expectation values, even in materials with simple cubic crystal structure such as Ba2NaOsO6. Experimental tests of these theories by local probes are highly sought for. Our local measurements designed to concurrently probe spin and orbital/lattice degrees of freedom of Ba2NaOsO6 provide such tests. Here we show that a canted ferromagnetic phase which is preceded by local point symmetry breaking is stabilized at low temperatures, as predicted by quantum theories involving multipolar spin interactions.