Josephson (001) tilt grain boundary junctions of high temperature superconductors

TL;DR

This study models the critical current in high-temperature superconductor grain boundary junctions, revealing how Fermi surface topology and tunneling processes influence phase-sensitive experimental interpretations.

Contribution

It provides a detailed theoretical analysis of in-plane (001) tilt grain boundary junctions, considering various doping types, order parameters, and tunneling models, clarifying the interpretation of phase-sensitive experiments.

Findings

Symmetric junctions with random tunneling align with Sigrist-Rice theory.

Specular tunneling results depend on Fermi surface topology.

Asymmetric hole-doped junctions show Fermi surface and tunneling details are crucial.

Abstract

We calculate the critical current $I_c$ across in-plane (001) tilt grain boundary junctions of high temperature superconductors. We solve for the electronic states corresponding to the electron-doped cuprates, two slightly different hole-doped cuprates, and an extremely underdoped hole-doped cuprate in each half-space, and weakly connect the two half-spaces by either specular or random quasiparticle tunneling. We treat symmetric, straight, and fully asymmetric junctions with s-, extended-s-, or d$_{x^2-y^2}$-wave order parameters. For symmetric junctions with random grain boundary tunneling, our results are generally in agreement with the Sigrist-Rice form for ideal junctions that has been used to interpret ``phase-sensitive'' experiments consisting of such in-plane grain boundary junctions. For specular grain boundary tunneling across symmetric juncitons, our results depend upon the Fermi surface topology, but are usually rather consistent with the random facet model of Tsuei {\it et al.} [Phys. Rev. Lett. {\bf 73}, 593 (1994)]. Our results for asymmetric junctions of electron-doped cuparates are in agreement with the Sigrist-Rice form. However, ou resutls for asymmetric junctions of hole-doped cuprates show that the details of the Fermi surface topology and of the tunneling processes are both very important, so that the ``phase-sensitive'' experiments based upon the in-plane Josephson junctions are less definitive than has generally been thought.