Determinations Of Upper Critical Fields In Continuous Ginzburg–Landau Model

Novel procedures to determine the parallel upper critical fieldBc2(one-dimensional, 1D) have been proposed within a continuous Ginzburg–Landau model. Unlike conventional methods, whereBc2is obtained through the determination of the smallest eigenvalue of an appropriate eigen equation, the square of the magnetic field is treated as eigenvalue problems by two procedures so that the upper critical field can be directly deduced. The two procedures proposed are extended to determine the upper critical field in thec–acrystal plane (two-dimensional, 2D) with an arbitrary angle θ tilted from thec-axis.The calculatedBc2from the two procedures are consistent with each other in both 1D and 2D cases. Moreover, the values ofBc2near the direction parallel to the layers obtained in the 2D case well approximate the counterparts in the 1D case. The properties of the calculatedBc2are in reasonably good agreement with existing theories and experiments. The profiles of the order parameters associated withBc2for both 1D and 2D cases are Gaussian-like, further validating the methodology proposed.