Superconducting Fluctuations and the Pseudogap in the Slightly Overdoped High- $T_c$ Superconductor ${\mathrm{TlSr}}_2{\mathrm{CaCu}}_2{O}_{6.8}$: High Magnetic Field NMR Studies

From measurements of the ${}^{63}\mathrm{Cu}$ Knight shift ( $K$) and the nuclear spin-lattice relaxation rate ( $1/T_1$) under magnetic fields from zero up to 28 T in the slightly overdoped high- $T_c$ superconductor ${\mathrm{TlSr}}_2{\mathrm{CaCu}}_2{\mathrm{O}}_{6.8}$ ( $T_c=68\mathrm{}\mathrm{K}$), we find that the pseudogap behavior, i.e., the reductions of $1/T_{1}T$ and $K$ above $T_c$ from the values expected from the normal state at high $T$, is strongly field dependent and follows a scaling relation. We show that this scaling is consistent with the effects of the Cooper pair density fluctuations. The present finding contrasts sharply with the pseudogap property reported previously in the underdoped regime where no field effect was seen up to 23.2 T. The implications are discussed.