Abstract
The upper critical fields in high temperature cuprates, heavy Fermion superconductors and organic superconductors have been studied intensively. The low dimensionality of these materials effectively suppresses the spin-orbit coupling for field close to the plane direction, so the Pauli paramagnetic limiting can take an important role. Upper critical fields exceeding the BCS limit have been frequently reported. Such high fields have been attributed to unconventional pairing (e.g. triplet pairing or p-wave), and the enhanced Pauli limit by strong spin-orbital scattering, or a non uniform superconducting Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state. There have been many theoretical works on the FFLO state. But up to date, no indisputable experimental evidence has ever been found due to the stringent requirements for the FFLO state to appear. To probe the upper critical field and the possible existence of FFLO state in the organic superconductor kappa(BEDT-TTF) 2Cu[N(CN)2]Br, we did a series of magnetoresistance measurements. In addition to the finding of an in-plane upper critical field exceeding the BCS Pauli limit, we discovered a first order phase transition between the superconducting state and normal state at low temperature for field close to plane direction. The agreement of our findings with the theoretic prediction indicates a possible existence of FFLO state in the title compound at clean limit.