Effect of Proximity Coupling of Chains and Planes on the Penetration Depth Anisotropy in Y_1Ba_2Cu_3O_7

TL;DR

This paper investigates how the coupling between CuO chains and CuO$_2$ planes in YBa$_2$Cu$_3$O$_7$ affects the anisotropy of penetration depth, revealing limitations of simple proximity models in explaining chain superfluidity.

Contribution

The study demonstrates that a basic proximity coupling model cannot fully explain the superfluid behavior observed in the chains of YBa$_2$Cu$_3$O$_7$.

Findings

Penetration depth anisotropy varies with temperature along different crystallographic directions.

Proximity model predicts different temperature dependence for chain and plane directions.

Experimental data shows nearly identical temperature dependence, challenging the simple proximity model.

Abstract

We calculate the penetration depth $\lambda$ in the $a$, $b$ and $c$ directions for a simple model of YBa$_2$Cu$_3$O$_7$. In this model there are two layers---representing a CuO$_2$ plane and a CuO chain---per unit cell. There is a BCS--like pairing (both $s$ wave and $d$ wave are considered) interaction localised in the CuO$_2$ planes. The CuO chains become superconducting at temperatures lower than $T_c$ because of their proximity to the planes, and there is an induced gap in the chains. Since the temperature dependence of the penetration depth in the $b$ direction (along the chains) is sensitive to the size of the induced gap, the difference between the shapes of the penetration depth curves in the $a$ and $b$ directions reveals a great deal about the nature of the condensate in the chains. We find that in our proximity model there are always regions of the chain Fermi surface on which the induced gap is much smaller than $T_c$, so that the temperature dependence of $\lambda_b$ is always different than that of $\lambda_a$. Experimental observations of the of the $ab$ anisotropy show nearly identical temperature dependences. The main result of our paper, then, is that a simple proximity model in which the pairing interaction is localized to the planes, and the planes are coherently coupled to the chains cannot account for the superfluid on the chains.