In this study, we have constructed an extended version of Ginzburg-Landau theory of superconductivity starting from the exponential non-standard Lagrangian. An extended Ginzburg-Landau coherence length and an extended Ginzburg-Landau parameter emerge in the theory without affecting the Abrikosov's fluxoid quantization law. We have discussed the Abrikosov's periodic vortex lattice problem and we have observed that plausible solutions give rise to a shrink in the energy levels. We have also found that a transition between a type-II and a type-I superconductor takes place for$\kappa =\sqrt{2}/2$whereas a transition between a new type-III and a type-I superconductor takes place for $\kappa =\zeta \sqrt{2}/4$ where $\zeta$ is a physical parameter. The new effective field of type III puts a supplementary limit for supercooling of the normal phase in superconductors. It was also revealed that a geometric transition from the square lattice to the rectangular lattice, a phenomenon which is detected in a number of superconductor's states.

在这项研究中，我们从指数非标准拉格朗日算子开始构造了Ginzburg-Landau超导理论的扩展版本。理论中出现了扩展的Ginzburg-Landau相干长度和扩展的Ginzburg-Landau参数，而不会影响Abrikosov的通量量化定律。我们已经讨论了Abrikosov的周期性涡旋晶格问题，并且已经观察到合理的解会引起能级的减小。我们还发现，II型和I型超导体之间发生了过渡$\kappa =\sqrt{2}/2$而新的III型和I型超导体之间发生了过渡 $\kappa =\zeta \sqrt{2}/4$ 哪里 $\zeta$是一个物理参数。III型的新有效领域为超导体中正相的过冷设定了补充限制。还揭示出从正方形晶格到矩形晶格的几何过渡，这种现象在许多超导体状态中被检测到。