Carrier-Concentration Dependence of the Pseudogap Ground State of Superconducting ${\mathrm{Bi}}_2{\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{CuO}}_{6+\delta }$ Revealed by ${}^{63,65}\mathrm{Cu}$-Nuclear Magnetic Resonance in Very High Magnetic Fields

We report the results of the Knight shift by ${}^{63,65}\mathrm{Cu}$-NMR measurements on single-layered copper-oxide ${\mathrm{Bi}}_2{\mathrm{Sr}}_{2-x}{\mathrm{La}}_x{\mathrm{CuO}}_{6+\delta }$ conducted under very high magnetic fields up to 44 T. The magnetic field suppresses superconductivity completely, and the pseudogap ground state is revealed. The ${}^{63}\mathrm{Cu}$-NMR Knight shift shows that there remains a finite density of states at the Fermi level in the zero-temperature limit, which indicates that the pseudogap ground state is a metallic state with a finite volume of Fermi surface. The residual density of states in the pseudogap ground state decreases with decreasing doping (increasing $x$) but remains quite large even at the vicinity of the magnetically ordered phase of $x\ge 0.8$, which suggests that the density of states plunges to zero upon approaching the Mott insulating phase.

Figure 1

$T$ dependence of the ${}^{63}\mathrm{Cu}$ Knight shift ($H\parallel c$) for $x=0.40$ measured under different magnetic fields. The solid and dotted arrows indicate the pseudogap temperature $T^{*}$ and superconducting $T_c$ ($H=7\mathrm{T}$), respectively. The dotted line is a guide to the eye.

Figure 2

$T$ dependence of $K_c$ for $0.0\le x\le 0.75$. The open symbols are results measured at 9 T. The closed symbols are taken at different fields as follows: 30 (for all $x\ge 0.15$), 21.7 (for $x=0.65$ and 0.75), and 44 T (for $x=0.40$). The solid arrows indicate the pseudogap temperature $T^{*}$. The dotted lines are guides to the eye. The dotted arrow indicates the value of $K_{\mathrm{orb}}$ (see text).

Figure 3

Field dependence of $K_c$ and $K_c-K_{\mathrm{dia}}$ for $x=0.40$. The dotted and solid curves are fittings assuming $K_c(H)-K_{\mathrm{dia}}\propto \sqrt{H}$ in the absence of impurity scattering and $K_c(H)-K_{\mathrm{dia}}\propto \frac{H}{H_{c2}}\ln (\frac{H_0}{H})$ in the presence of impurity scattering, respectively.

Figure 4

(a) $T$ dependences of $I(T)\times T$ for $x=0.75$, 0.80, and 0.90, respectively. The data are normalized by the value at high temperatures. The dotted line is a guide to the eye. The arrows indicate $T_N$. (b) Zero-field ${}^{63,65}\mathrm{Cu}$-NMR spectrum above and below $T_N$ for $x=0.90$. The solid curve is a fit to a model described in the text.

Figure 5

The upper panel shows characteristic temperatures vs $1-x$ ($\propto \mathrm{\text{hole}}$ concentration). For $x=0.90$ and 0.80, no superconductivity occurs (open squares). The open circles are taken from Refs. 4, 29. The lower panel shows the hole-concentration dependence of relative DOS at $T=0$.