Determinations of upper critical fields in continuous Ginzburg-Landau model

Abstract

Novel procedures to determine the parallel upper critical field B c2 (one-dimensional, 1D) have been proposed within a continuous Ginzburg-Landau model. Unlike conventional methods, where Bc2 is 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 the c-a crystal plane (two-dimensional, 2D) with an arbitrary angle θ tilted from the c-axis. The calculated Bc2 from the two procedures are consistent with each other in both 1D and 2D cases. Moreover, the values of Bc2 near the direction parallel to the layers obtained in the 2D case well approximate the counterparts in the 1D case. The properties of the calculated Bc2 are in reasonably good agreement with existing theories and experiments. The profiles of the order parameters associated with Bc2 for both 1D and 2D cases are Gaussian-like, further validating the methodology proposed.