Fulde-Ferrell-Larkin-Ovchinnikov State in the Organic Superconductor κ-(BEDT-TTF)₂Cu(NCS)₂

extraordinary high and the Pauli limit becomes of importance instead. For this case the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state was theoretically predicted. It is now 55 years that this state is being looked for experimentally. The most promising candidates are layered superconductors such as the organic compound κ-(BEDT-TTF)₂Cu(NCS)₂. When the field is applied parallel to the layers, the orbital limit exceeds the Pauli limit at 22 T. I will present specific heat and magnetic torque experiments up to 30 T and down to 50 mK. The upper critical field transition changes from second to first-order nature above 21 T, the transition line shows a characteristic upturn and a novel transition line separates an unconventional high-field SC phase from the conventional low-field phase. Additional transitions are observed in slightly tilted angles, suggesting a rich physics with a competition between orbital and Pauli limits. These results provide strong evidence for the FFLO state in κ-(BEDT-TTF)₂Cu(NCS)₂.