Scaling behavior of layered high-(formula presented) superconductors with columnar defects

It was recently observed [van der Beek et al., Phys. Rev. B (formula presented) R792 (1996)] that irradiated layered high-(formula presented) superconductors subject to perpendicular magnetic field manifest two similar scaling behaviors corresponding to two different critical temperatures. We show that this phenomenon is explained within the framework of the Ginzburg-Landau theory. In the weak field region, the scaling function differs from that of a clean sample mainly because of the renormalization of the critical temperature, due to defects. In the strong field region, defects are effectively suppressed and the scaling function, as well as the critical temperature, are the same as in a clean superconductor. The theory presented here agrees quite satisfactory with experiment.