Theory of Upper Critical Field without Energy Quantization

TL;DR

This paper introduces a novel theoretical approach to calculating the upper critical magnetic field in superconductors, avoiding traditional energy quantization methods, and successfully explains the upward curvature phenomenon observed in experiments.

Contribution

It presents an alternative theory for upper critical fields that aligns with Ginzburg-Landau results and explains the upward curvature as a crossover of the order parameter.

Findings

The new theory agrees with Ginzburg-Landau predictions.

Explains the upward curvature of the upper critical field.

Provides an alternative to energy quantization methods.

Abstract

Conventional theories for determining upper critical fields are inevitably related to the lowest eigenvalues of appropriate equations. In this Letter, a new theory of upper critical fields is designed and justified. Using MgB$_2$ as modeling prototype, our computations are in excellent agreement with the Ginzburg-Landau theory. The long-standing issue, the upward curvature of the upper critical field, is found to be a manifestation of the crossover of the order parameter. The current theory is an alternative to the traditional technique of energy quantization in determining upper critical fields.