UCLA

Due to the low dimensionality of molecular conductors, they are categorized into a class of materials with strong electron correlation, namely Coulomb repulsion. The pairing mechanism of unconventional superconductors (SCs), which commonly arises in these compounds, is a central and unresolved problem in condensed matter physics. Whereas numerous unconventional SCs exist in the vicinity of magnetic ground states, we investigate whether magnetic ordering or fluctuation is a necessary ingredient of unconventional superconductivity, as well as whether other mechanisms such as the charge degree of freedom can play a role. Moreover, the low dimensionality of molecular conductors also allows us to study a long-sought-after inhomogeneous high field superconducting phase, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. $\beta"$-(BEDT-TTF)$_2$SF$_5$CH$_2$CF$_2$SO$_3$ ($\beta"$-SC) that belongs to the family of molecular conductors, is an ideal candidate for studies of both topics. Nuclear magnetic resonance (NMR) is one of the few possible microscopic experimental probes for studying molecular conductors. In this dissertation, interesting physics in $\beta"$-SC, in the contexts such as charge-fluctuation mediated superconductivity and the fluctuating nature of the FFLO state, is revealed by NMR.

Specifically, our results on $\beta"$-SC are consistent with an unconventional superconducting state with singlet pairing and nodal superconducting gap. Moreover, absent or barely distinguishable evidence of magnetic fluctuations are observed above superconducting transition temperature $T_c$, unlike in most other unconventional SCs, including high $T_c$ cuprate SCs. In the normal state, $\beta"$-SC is a charge-ordered metal revealed by NMR spin lattice relaxation rate $(T_1T)^{-1}$. The charge disproportionation forms a stripe pattern along the $a$ axis, whereas the disproportionation increases monotonically upon cooling to $T_c$. Above $T_c$, $\beta"$-SC exhibits only moderate antiferromagetic correlation from analysis of Korringa ratio $\varkappa\sim2$. Motion of the ethylene end groups is studied by $^2$H NMR above 100 K, and is found to induce an enhanced $(T_1T)^{-1}$ on $^{13}$C through modifying the electron correlation. The response of $(T_1T)^{-1}$ to pressure shows that charge disproportionation is suppressed at high pressures as well as $T_c$ according to previous reports, indicating the possible interplay between charge disproportionation and superconductivity.

In the FFLO state, when the orbital pair breaking effect is suppressed under in-plane magnetic field, we observe an unusual enhancement of $(T_1T)^{-1}$ above the normal state $(T_1T)^{-1}$, at the verge of the FFLO--uniform SC phase boundary. Moreover, we observe an enhancement that is 2.5 times the normal state $(T_1T)^{-1}$ under 1 degree misaligned field at $B=9.25$ T. We conclude that both in-plane and out-of-plane $(T_1T)^{-1}$ enhancements in the FFLO state originate from hyperfine coupling to the electrons. We propose a picture of a fluctuating FFLO state where the enhancement of $(T_1T)^{-1}$ is caused by a fluctuating magnetic field induced by dynamics of short-range modulations of the superconducting order parameter.