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Superconductivity is a quantum phenomena arising, in its simplest form, frompairing of fermions with opposite spin into a state with zero net momentum.Whether superconductivity can occur in fermionic systems with unequal number oftwo species distinguished by spin, atomic hyperfine states, flavor, presents animportant open question in condensed matter, cold atoms, and quantumchromodynamics, physics. In the former case the imbalance between spin-up andspin-down electrons forming the Cooper pairs is indyced by the magnetic field.Nearly fifty years ago Fulde, Ferrell, Larkin and Ovchinnikov (FFLO) proposedthat such imbalanced system can lead to exotic superconductivity in which pairsacquire finite momentum. The finite pair momentum leads to spatiallyinhomogeneous state consisting of of a periodic alternation of "normal" and"superconducting" regions. Here, we report nuclear magnetic resonance (NMR)measurements providing microscopic evidence for the existence of this newsuperconducting state through the observation of spin-polarized quasiparticlesforming so-called Andreev bound states.

Evidence of Andreev bound states as a hallmark of the FFLO phase in $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$