Zeeman and Orbital Effects of an in-Plane Magnetic Field in Cuprate Superconductors

TL;DR

This paper analyzes how in-plane magnetic fields affect high-temperature cuprate superconductors, highlighting differences between in-plane and inter-layer superconductivity mechanisms and estimating the upper critical field.

Contribution

It provides a theoretical comparison of Zeeman and orbital effects in layered superconductors, emphasizing the distinct impacts on different superconductivity mechanisms.

Findings

Zeeman effect dominates at high magnetic fields for in-plane mechanisms.

Orbital effects differ significantly between in-plane and inter-layer mechanisms.

Estimated upper critical field $H_{c2}$ for suppressing superconductivity.

Abstract

We discuss the effects of a magnetic field applied parallel to the Cu-O ($ab$) plane of the high $T_c$ cuprate superconductors. After briefly reviewing the Zeeman effect of the field, we study the orbital effects, using the Lawrence-Doniach model for layered superconductors as a guide to the physics. We argue that the orbital effect is qualitatively different for in-plane and inter-layer mechanisms for superconductivity. In the case of in-plane mechanisms, interlayer couplings may be modeled as a weak interlayer Josephson coupling, whose effects disappear as $H\to\infty$; in this case Zeeman dominates the effect of the field. In contrast, in the inter-layer mechanism the Josephson coupling {\em is} the driving force of superconductivity, and we argue that the in-plane field suppresses superconductivity and provides an upper bound for $H_{c2}$ which we estimate very crudely.