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We present upper critical field data for $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$with the magnetic field close to parallel and parallel to the conductinglayers. We show that we can eliminate the effect of vortex dynamics in theselayered materials if the layers are oriented within 0.3 degrees of parallel tothe applied magnetic field. Eliminating vortex effects leaves one remainingfeature in the data that corresponds to the Pauli paramagnetic limit ($H_p$).We propose a semi-empirical method to calculate the $H_p$ in quasi 2Dsuperconductors. This method takes into account the energy gap of each of thequasi 2D superconductors, which is calculated from specific heat data, and theinfluence of many body effects. The calculated Pauli paramagnetic limits arethen compared to critical field data for the title compound and other organicconductors. Many of the examined quasi 2D superconductors, including the aboveorganic superconductors and CeCoIn$_5$, exhibit upper critical fields thatexceed their calculated $H_p$ suggesting unconventional superconductivity. Weshow that the high field low temperature state in$\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$ is consistent with the Fulde Ferrell LarkinOvchinnikov state.

physical review. b, condensed matter and materials physics

An Experimental and Semi-Empirical Method to Determine the  Pauli-Limiting Field in Quasi 2D Superconductors as applied to  $\kappa$-(BEDT-TTF)$_2$Cu(NCS)$_2$: Strong Evidence of a FFLO State