Exact solution of the Ginzburg-Landau equation for the upper critical field of a dx2-y2 superconductor

A d(x2-y2) superconductor is modeled as the superconducting layers in the a-b plane, whose coupling in the c direction is approximated by the effective mass, within the Ginzburg-Landau theory. In this work, this model is applied to the system where the, coherence length along the c direction is greater than the layer spacing. Based on our model, we calculate the upper critical field in a magnetic field lying in a-e plane and tilted by an angle from the c axis. According to our results, the curvature of H-c2(T) is upward, and the slope - dH(c2)(T)/dT depends on the angle between the c axis and the external field. The most interesting feature is that the ratio of the c-direction parameter related to the effective mass to the n-b plane parameter connected with the effective mass can influence H-c2. As the rafio is decreased, H-c2. becomes increased. We also find that there is no admixture of s-wave component in the critical regime and believe that the upward curvature of the H-c2(T) is the characteristic property of a d-wave superconductor. [S0163-1829(99)01914-1].