Two types of superconducting pairs in stripe-ordered La${}_{2-x}$Ba${}_x$CuO${}_4$ ($x=1\mathrm{/}8$): evidence from the resistivity measurements

Recent angle-resolved $c$-axis resistivity measurements of the stripe-ordered La${}_{2-x}$Ba${}_x$CuO${}_4$ (LBCO) with $x=1\mathrm{/}8$ revealed an unexpected dependence on the direction of the in-plane magnetic field. We argue that these and other available data for the $c$-axis transport point to the existence of superconducting pairs of two different types in the $x=1\mathrm{/}8$ LBCO below the stripe ordering temperature. The pairs of one type carry finite momentum and are confined to the Cu-O planes; the pairs of other type (probably the conventional $d$-wave with zero momentum) propagate along narrow conducting channels traversing the sample in the $c$-axis direction. The evidence for this comes from the observed exponential temperature dependence of the $c$-axis resistivity ${\rho }_c(T)$ which we attribute to the thermally excited slips of the superconducting phase and flux flows. We present a simple theory to fit the observed $\pi \mathrm{/}2$-periodic dependence of ${\rho }_c$ on the direction of the in-plane magnetic field and the other data.