Critical Point and the Nature of the Pseudogap of Single-Layered Copper-Oxide ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_{2-x}{\mathrm{L}\mathrm{a}}_x\mathrm{C}\mathrm{u}{\mathrm{O}}_{6+\delta }$ Superconductors

We apply strong magnetic fields of $H=28.5$ to 43 T to suppress superconductivity (SC) in the cuprates ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_{2-x}{\mathrm{L}\mathrm{a}}_x\mathrm{C}\mathrm{u}{\mathrm{O}}_{6+\delta }$ ($x=0.65$, 0.40, 0.25, 0.15, and 0), and investigate the low temperature ($T$) normal state by ${}^{63}\mathrm{C}\mathrm{u}$ nuclear spin-lattice relaxation rate ($1/T_1$) measurements. We find that the pseudogap (PG) phase persists deep inside the overdoped region but terminates at $x\sim 0.05$, which corresponds to the hole doping concentration of approximately 0.21. Beyond this critical point, the normal state is a Fermi liquid that persists as the ground state when superconductivity is removed by the magnetic field. A comparison of the superconducting state with the $H$-induced normal state in the $x=0.40$ ($T_c=32\mathrm{K}$) sample indicates that there remains substantial part of the Fermi surface even in the fully developed PG state, which suggests that the PG and SC are coexisting matters.

Figure 1

The quantity $1/T_{1}T$ plotted against $T$ for ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_{2-x}{\mathrm{L}\mathrm{a}}_x\mathrm{C}\mathrm{u}{\mathrm{O}}_{6+\delta }$ measured at a field of 28.5 T applied along the $c$ axis.

Figure 2

Magnetic field dependence of $1/T_{1}T$ for ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_{1.6}{\mathrm{L}\mathrm{a}}_{0.4}\mathrm{C}\mathrm{u}{\mathrm{O}}_{6+\delta }$. The arrow indicates $T_c$ at zero magnetic field.

Figure 3

Magnetic field dependence of $1/T_{1}T$ for the as-grown, overdoped sample, ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_2\mathrm{C}\mathrm{u}{\mathrm{O}}_{6+\delta }$. The arrow indicates $T_c$ at zero magnetic field.

Figure 4

Phase diagram obtained from NMR measurements for ${\mathrm{B}\mathrm{i}}_2{\mathrm{S}\mathrm{r}}_{2-x}{\mathrm{L}\mathrm{a}}_x\mathrm{C}\mathrm{u}{\mathrm{O}}_{6+\delta }$. $T^{*}$ is the temperature below which the pseudogap develops, and $T_c$ is the superconducting transition temperature. The upper scale of the transverse axis is adopted from Ref. 22. PG and SC denote the pseudogap phase and superconducting phase, respectively.