  We study the critical charge dynamics of the superconducting to the
normal-state transition for LSCO thin films with a wide range of the Sr
concentration, by measuring the frequency-dependent excess parts of the complex
microwave conductivity, which is induced by the superconducting fluctuations.
We present a dynamic scaling analysis of the complex fluctuation conductivity,
which includes the information on the universality class and the dimensionality
of the critical charge dynamics as a function of the Sr concentration, the film
thickness and the magnetic field. In our previous study (H. Kitano et al.,
Phys. Rev. B 73, 092504 (2006).), the 2D-XY critical dynamics for underdoped
LSCO and the 3D-XY critical dynamics for optimally doped LSCO were reported. In
this study, we observed a novel two-dimensional unknown critical charge
dynamics for overdoped thin films from x=0.17 to 0.20, which is clearly
distinguished from the 2D-XY critical dynamics. Through the systematic
measurements by changing the film thickness or by applying small magnetic
field, it was confirmed that this unusual behavior, which is referred as 2D-"U"
below, was not induced by the finite size effect but was intrinsic to the
overdoped LSCO. Thus, it was found that the critical behavior in the phase
diagram of LSCO is classified into the following three types; (i) 2D-XY for
underdoped region, (ii) 3D-XY for optimally doped region, and (iii) 2D-"U" for
overdoped region. In other words, the dimensionality in the critical charge
dynamics is changed twice with hole doping. We discuss possible origins of such
anomalous dimensional crossovers with hole doping, including an interpretation
based on the possible existence of a hidden quantum critical point near the
optimally doped region.
