Superconducting fluctuation of La$_{2-x}$Sr$_x$CuO$_4$ thin films probed by THz conductivity measurement

In high-$T_c$ cuprate superconductor, Nernst signal appears far above $T_c$ in the underdoped region, which was suggested as the manifestation of vortex-like precursor of the superconducting transition.\footnote{Z. A. Xu {\it et al.}, Nature {\bf 406}, 486 (2000).} On the other hand, we previously investigated the superconducting fluctuation by measuring the microwave complex conductivity of La$_{2-x}$Sr$_x$CuO$_4$ (LSCO) thin films, and found a different analytical result that the superconducting fluctuation exists up to $T \sim 2 T_c$ at most, even at the infinite frequency.\footnote{H. Kitano {\it et al.}, Phys. Rev. {\bf B73}, 092504 (2006); T. Ohashi {\it et al.}, Phys. Rev. {\bf B79}, 184507 (2009).} To resolve this discrepancy, we directly measured the THz conductivity on LSCO thin films with various doping level ($x$ = 0.07, 0.12, 0.15, 0.225). We found that the imaginary part of the complex conductivity increases rapidly from the temperature about $T \sim 2 T_c$ at most, which is consistent with the result of our microwave measurement. This result suggests that the appearance of large Nernst signal in high-$T_c$ superconductor is not caused by superconducting fluctuation.