Variational method to study vortex matter in mesoscopic superconductors

TL;DR

This paper introduces a variational model to analyze vortex states in mesoscopic cylindrical type-II superconductors, enabling solutions to Ginzburg-Landau equations and mapping phase transitions under magnetic fields.

Contribution

It presents a simple variational approach to study vortex matter and phase diagrams in mesoscopic superconductors, including critical fields and magnetization behavior.

Findings

Derived the equilibrium phase diagram for thin cylinders.

Calculated the lower critical magnetic field for arbitrary cylinder sizes.

Analyzed the field dependence of magnetization in multi-quantum vortex states.

Abstract

A simple variational model is proposed to analyze the superconducting state in long cylindrical type-II superconductor placed in the external magnetic field. In the framework of this model, it is possible to solve the Ginzburg-Landau equations for the states with axially symmetric distributions of the order parameter. Phase transitions between different superconducting states are studied in the presence of external magnetic field and an equilibrium phase diagram of thin cylinder is obtained. The lower critical field of the cylindrical type-II superconductor with arbitrary values of radius and Ginzburg-Landau parameter is found. The field dependence of the magnetization of thin cylinder, which can carry several magnetic flux quanta, is calculated.