A microscopic model for the intrinsic Josephson tunneling in high-T_C superconductors

TL;DR

This paper presents a microscopic model based on interlayer tunneling and a 2-D Hubbard model to analyze intrinsic Josephson effects in high-temperature superconductors, showing sinusoidal flux dependence and mild temperature effects.

Contribution

It introduces a detailed microscopic model combining Hubbard planes and flux threading to explain Josephson tunneling in high-T_C superconductors, aligning with experimental observations.

Findings

Current exhibits sinusoidal dependence on magnetic flux.

Supercurrent temperature dependence shows only mild elevation of transition temperature.

Model results are compared with BCS theory and experimental data.

Abstract

A quantitative analysis of a microscopic model for the intrinsic Josephson effect in high-temperature superconductors based on interlayer tunneling is presented. The pairing correlations in the CuO_2-planes are modelled by a 2-D Hubbard-model with attractive interaction, a model which accounts well for some of the observed features such as the short planar coherence length. The stack of Hubbard planes is arranged on a torus, which is threaded by a magnetic flux. The current perpendicular to the planes is calculated as a function of applied flux (i. e. the phase), and -- after careful elimination of finite-size effects due to single-particle tunneling -- found to display a sinusoidal field dependence in accordance with interlayer Josephson tunneling. Studies of the temperature dependence of the supercurrent reveal at best a mild elevation of the Josephson transition temperature compared to the planar Kosterlitz-Thouless temperature. These and other results on the dependence of the model parameters are compared with a standard BCS evaluation.