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Superconducting Fluctuation investigated by THz Conductivity of La$_{2-x}$Sr$_x$CuO$_4$ Thin Films

Frequency-dependent terahertz conductivities of La$_{2-x}$Sr$_x$CuO$_4$ thin films with various carrier concentrations were investigated. The imaginary part of the complex conductivity considerably increased from far above a zero-resistance superconducting transition temperature, $T_\text{c}^\text{zero}$, because of the existence of the fluctuating superfluid density with a short lifetime. The onset temperature of the superconducting fluctuation is at most $\sim 2T_\text{c}^\text{zero}$ for underdoped samples, which is consistent with the previously reported analysis of microwave conductivity. The superconducting fluctuation was not enhanced under a 0.5 T magnetic field. We also found that the temperature dependence of the superconducting fluctuation was sensitive to the carrier concentration of La$_{2-x}$Sr$_x$CuO$_4$, which reflects the difference in the nature of the critical dynamics near the superconducting transition temperature. Our results suggest that the onset temperature of the Nernst signal is not related to the superconducting fluctuation we argued in this paper.