Upper critical field $H_{c2}$ calculations for the high critical temperature superconductors considering inhomogeneities

TL;DR

This paper models the upper critical field in high-temperature superconductors by incorporating intrinsic inhomogeneities and a percolation framework, explaining anomalies in experimental observations.

Contribution

It introduces a novel approach using an average linearized Ginzburg-Landau equation considering charge density inhomogeneities to calculate $H_{c2}$ in HTSC.

Findings

Explains high-temperature anomalies in $H_{c2}$, Meissner, and Nernst effects.

Models the transition as a percolation among regions with different $T_c$.

Provides a theoretical framework aligning with experimental data.

Abstract

We perform calculations to obtain the $H_{c2}$ curve of high temperature superconductors (HTSC). We consider explicitly the fact that the HTSC possess intrinsic inhomogeneities by taking into account a non uniform charge density $\rho(r)$. The transition to a coherent superconducting phase at a critical temperature $T_c$ corresponds to a percolation threshold among different superconducting regions, each one characterized by a given $T_c(\rho(r))$. Within this model we calculate the upper critical field $H_{c2}$ by means of an average linearized Ginzburg-Landau (GL) equation to take into account the distribution of local superconducting temperatures $T_c(\rho(r))$. This approach explains some of the anomalies associated with $H_{c2}$ and why several properties like the Meissner and Nernst effects are detected at temperatures much higher than $T_c$.