Metal-to-insulator crossover and pseudogap in single-layer ${\mathrm{Bi}}_{2+x}{\mathrm{Sr}}_{2-x}{\mathrm{Cu}}_{1+y}{\mathrm{O}}_{6+\delta }$ single crystals in high magnetic fields

The in-plane ${\rho }_{ab}\left(H\right)$ and the out-of-plane ${\rho }_c\left(H\right)$ magneto-transport in magnetic fields up to $28\mathrm{T}$ has been investigated in a series of high quality, single crystal, hole-doped La-free Bi2201 cuprates for a wide doping range and over a wide range of temperatures down to $40\mathrm{mK}$. With decreasing hole concentration going from the overdoped $(p=0.2)$ to the underdoped $(p=0.12)$ regimes, a crossover from a metallic to an insulating behavior of ${\rho }_{ab}\left(T\right)$ is observed in the low temperature normal state, resulting in a disorder induced metal insulator transition. In the zero temperature limit, the normal state ratio ${\rho }_c\left(H\right)∕{\rho }_{ab}\left(H\right)$ of the heavily underdoped samples in pure Bi2201 shows an anisotropic 3-D behavior, in striking contrast with that observed in La-doped Bi2201 and LSCO systems. Our data strongly support that the negative out-of-plane magnetoresistance is largely governed by interlayer conduction of quasiparticles in the superconducting state, accompanied by a small contribution of normal state transport associated with the field dependent pseudogap. Both in the optimal and overdoped regimes, the semiconducting behavior of ${\rho }_c\left(H\right)$ persists even for magnetic fields above the pseudogap closing field $H_{\mathit{pg}}$. The method suggested by [Shibauchi et al. Phys. Rev. Lett. 86, 5763 (2001)] for evaluating $H_{\mathit{pg}}$ is unsuccessful for both under- and overdoped Bi2201 samples. Our findings suggest that the normal state pseudogap is not always a precursor of superconductivity.

Figure 1

Temperature dependence of the in-plane resistivity $\left({\rho }_{ab}\right)$ as function of temperature for Bi2201 samples with different hole concentrations. The inset shows the critical temperature for superconductivity $\left(T_c\right)$ determined from ${\rho }_{ab}$ as a function of the hole concentration.

Figure 2

Semi-log plot of ${\rho }_{ab}$ versus temperature for various magnetic fields applied along the $c$ axis for four Bi2201 samples with different hole concentrations.

Figure 3

In-plane resistance as a function of magnetic field applied along the $c$ axis (a) and in the $ab$ plane (b) measured at different temperatures for the underdoped Bi2201 sample with $p=0.12$.

Figure 4

$c$-axis resistivity ${\rho }_c$ as a function of temperature for Bi2201 samples with different hole concentrations. The inset shows the same data plotted on a semi-log scale.

Figure 5

${\rho }_c$ as a function of temperature and measured at various magnetic fields applied parallel to the $c$ axis for Bi2201 samples with different hole concentrations.

Figure 6

${\rho }_c$ as a function of the magnetic field applied parallel to the $c$ axis for different temperatures for Bi2201 samples with various hole concentrations. The inset in (c) shows the relative variation $\Delta {\rho }_c∕{\rho }_{c0}=[{\rho }_c(H,T)-{\rho }_c(0,T)]∕{\rho }_c(0,T)$ at different temperatures for both configurations at a magnetic field $H=28\mathrm{T}$. The inset in (d) shows the $c$-axis conductivity for the same sample $(p=0.2)$.

Figure 7

A log-log plot of ${\rho }_c$ versus the magnetic field for various temperatures for the overdoped Bi2201 samples.

Figure 8

${\rho }_c$ and ${\rho }_{ab}$ measured as a function of the magnetic field applied along the $c$ axis around $T=1.9\mathrm{K}$ for the (a) underdoped and (b) optimally doped Bi2201 samples.