Two-Dimensional Superconducting Fluctuations in Stripe-Ordered ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$

Recent spectroscopic observations of a $d$-wave-like gap in stripe-ordered ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ with $x=\frac{1}{8}$ have led us to critically analyze the anisotropic transport and magnetization properties of this material. The data suggest that concomitant with the spin ordering is an electronic decoupling of the ${\mathrm{CuO}}_2$ planes. We observe a transition (or crossover) to a state of two-dimensional (2D) fluctuating superconductivity, which eventually reaches a 2D superconducting state below a Berezinskii-Kosterlitz-Thouless transition. Thus, it appears that the stripe order in ${\mathrm{La}}_{2-x}{\mathrm{Ba}}_x{\mathrm{CuO}}_4$ frustrates three-dimensional superconducting phase order, but is fully compatible with 2D superconductivity and an enhanced $T_c$.

Figure 1

Experimental phase diagram for ${\mathrm{La}}_{1.875}{\mathrm{Ba}}_{0.125}{\mathrm{CuO}}_4$. The transition lines for charge order and spin order are from 11. The boundaries labeled $T_c^{2\mathrm{D}}$ and $T_{\mathrm{BKT}}$ are described in the text.

Figure 2

(a) Thermoelectric power vs temperature for several different magnetic fields [as labeled in (b)], applied along the $c$-axis. (b) In-plane resistivity vs temperature for the same magnetic fields as in (a). The vertical dashed line indicates $T_{\mathrm{co}}$.

Figure 3

(a) Ratio of ${\rho }_c$ to ${\rho }_{ab}$ vs temperature in fields of 0, 1 T, and 3 T, as labeled in (b). Inset shows zero-field resistivity vs temperature; note that ${\rho }_{ab}$ reaches zero (within error) at 18 K, while ${\rho }_c$ does not reach zero until 10 K. (b) In-plane resistivity vs temperature on a semilog scale, for three different $c$-axis magnetic fields, as labeled. The lines through the data points correspond to fits to Eq. (1). Inset shows ${\rho }_c$ at zero field on a linear scale.

Figure 4

(a) In-plane $V/I$ vs $I$ at five temperatures, as labeled. Note that $I$ is on a log scale. (b) Log-log plot of in-plane $V$ vs $I$ at temperatures from 20 to 10 K. Each curve is labeled by $T$ in K. Dashed lines are approximate fits to the slopes at low current; $\mathrm{\text{slope}}=p$. Inset: plot of $p$ vs $T$. Dashed line indicates that $p$ crosses 3 at $T=15.6\mathrm{K}$.

Figure 5

(a) ${\chi }_c$ vs temperature for several different magnetic fields, as labeled. (b) ${\chi }_{ab}$ vs temperature for several magnetic fields as labeled. Note that, for each applied field, measurements at temperatures lower than the plotted data range are unreliable due to excessive noise in this regime, possibly associated with the unusual state of the sample.