# Characterization of Electron Pair Velocity in YBa$_{2}$Cu$_{3}$O$_{7-\textit{$\delta $}}$ Thin Films

## TL;DR

This paper models the superconducting phase in YBCO thin films doped with CeO2 nanodots, focusing on electron pair velocity and flux vortex behavior to optimize nanodot deposition parameters.

## Contribution

A new model for characterizing the superconducting phase using electron pair work and chemical potential, based on established superconductivity theories.

## Key findings

- Model predicts optimal nanodot density and growth conditions.
- Analyzes flux vortex pinning effects on critical current.
- Provides theoretical framework for superconducting phase transition.

## Abstract

The superconducting phase transition in YBa$_{2}$Cu$_{3}$O$_{7-\textit{$\delta $}}$(YBCO) thin film samples doped with non-superconducting nanodot impurities of CeO$_{2}$ are the focus of recent high-temperature superconductor studies. Non-superconducting holes of the superconducting lattice induce a bound-state of circulating paired electrons. This creates a magnetic flux vortex state. Examining the flow of free-electrons shows that these quantized magnetic flux vortices arrange themselves in a self-assembled lattice. The nanodots serve to present structural properties to constrict the "creep" of these flux vorticies under a field response in the form of a pinning-force enhancing the critical current density after phase transition. In this work, a model for characterizing the superconducting phase by the work done on electron pairs and chemical potential, following the well-known theories of Superconductivity (Bardeen-Cooper-Scheifer \& Ginzburg-Landau), is formulated and tested.A solution to the expression for the magnetic flux, zero net force and pair velocity will generate a setting for the optimal deposition parameters of number density, growth geometry and mass density of these nanodot structures.