The Ground-state Inter-plane Superconducting Coherence Length of La${}_{1.875}$Sr${}_{0.125}$CuO${}_4$ Measured by a "Xiometer"

Abstract

A long excitation coil piercing a superconducting (SC) ring is used to generate ever increasing persistent current in the ring, until the current destroys the order parameter. Given that the penetration depth $\lambda$ is known, this experiment measures, hypothetically, the coherence length $\xi$, hence the name "Xiometer". We examine various aspects of this theoretically driven hypothesis by testing niobium rings with different dimensions, and by comparing the results to the known values of $\xi$. We then apply the method to two La${}_{1.875}$Sr${}_{0.125}$CuO${}_4$ rings at $T\to 0$. In one, the current flows in the CuO${}_2$ planes hence it is set by ${\xi }_{ab}$. In the other, the current must cross planes and is determined by ${\xi }_c$. We find that ${\xi }_c=1.3\pm 0.1$~nm, and ${\xi }_{ab}<2.3$nm indicating that at low temperatures the Cooper pairs are three dimensional.

6 pages with 7 figures