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. 
L. Wang, H. S. Lim, C. K. Ong