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Superconducting fluctuations probed by the Higgs mode in Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ thin films

Superconducting (SC) fluctuations in cuprate superconductors have been extensively studied to gain a deep insight into preformed Cooper pairs above the SC transition temperature $T_{\text{c}}$. While the various measurements, such as the terahertz (THz) optical conductivity, Nernst effect, angle-resolved photoemission spectroscopy (ARPES), and scanning tunneling microscopy (STM) measurements have provided the signature of the SC fluctuations, the onset temperature of the SC fluctuations depends on the measurement scheme. Here, we shed light on the Higgs mode to investigate the SC fluctuations, as it is the direct fingerprint of SC order parameter and can help elucidate the development of SC phase coherence. We perform THz pump-optical probe spectroscopy for underdoped and overdoped Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ (Bi2212) thin films. The oscillatory behavior in the pump-probe signal (THz Kerr signal) observed in the SC phase has been identified as the Higgs mode in single crystals in our previous work [K. Katsumi et al., Phys. Rev. Lett. 120, 117001 (2018)], but two onset temperatures are identified above $T_{\text{c}}$. Combined with the results of the single crystals in a wide range of doping, we find that the first onset $T_1^{\text{ons}}$ is 10-30 K above $T_{\text{c}}$. $T_1^{\text{ons}}$ coincides with that of the superfluid density $N_s$ extracted from the THz optical conductivity. Hence, $T_1^{\text{ons}}$ is interpreted as the onset of macroscopic SC phase stiffness. On the other hand, the second onset $T_2^{\text{ons}}$ is identified at substantially higher than $T_{\text{c}}$, whose origin is discussed in terms of preformed Cooper pairs.