Theory of Upper Critical Field without Energy Quantization

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.