Microscopic observation of superconducting fluctuations in $kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br by $^{13}$C NMR spectroscopy

We performed $^{13}$C-NMR experiment and measured spin-lattice relaxation rate divided by temperature $1/T_{1}T$ near the superconducting (SC) transition temperature $T_{c}$ in $kappa$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br ($kappa$-Br salt), and $kappa$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$ ($kappa$-NCS salt). We observed the reduction of $1/T_{1}T$ starting at the temperature higher than $T_c$ in $kappa$-Br salt. Microscopic observation of quasi-particle density of states in the fluctuating SC state revealed the effects of short-range Cooper pairs induced in the normal state to the quasi-particle density of states. We also performed systematic measurements in the fields both parallel and perpendicular to the conduction plane in $kappa$-Br and $kappa$-NCS salts, and confirmed that the reduction of $1/T_{1}T$ above $T_{c}$ is observed only in $kappa$-Br salt regardless of the external field orientation.