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

Superconductivity is a quantum phenomenon arising, in its simplest form, from the pairing of fermions with opposite spin into a state with zero net momentum. Whether superconductivity can occur in fermionic systems with an unequal number of two species distinguished by spin or flavour presents an important open question in condensed-matter physics or quantum chromodynamics(1). In condensed matter the imbalance between spin-up and spin-down electrons that form the Cooper pairs is induced by the magnetic field. Such an imbalanced system can lead to exotic superconductivity in which pairs acquire finite momentum(2,3). 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.