NMR evidence of weak Anderson localization in the organic superconductor ${\mathrm{\beta }}_{\mathit{L}}$-(ET${)}_2$${\mathrm{I}}_3$

We report on high-resolution variable-temperature ${}_{}{}^{13}{}_{}{}^{}\mathrm{C}$ magic-angle-spinning NMR spectra of the organic superconductor ${\mathrm{\beta }}_{\mathit{L}\mathrm{-}}$(ET${)}_2$ ${\mathrm{I}}_3$. Broadening of the resonances is observed when lowering the temperature, with onset near the incommensurate phase transition around 180 K inducing a static crystallographic disorder. The NMR line shape displays directly the spin distribution function in space. The results give evidence of weak Anderson localization. The theory of the Knight shift distribution in 2D disordered metal is presented. We determine the impurity scattering time of conduction electrons and use it to discuss the suppression of the superconducting transition temperature by the localization.