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Universal superconducting fluctuations and the implications for the phase diagram of the cuprates

Superconductivity in the cuprates emerges from an enigmatic metallic state. There remain profound open questions regarding the universality of observed phenomena and the character of precursor fluctuations above the superconducting (SC) transition temperature (T_c). For single-CuO_2-layer La_{2-x}Sr_xCuO_4 (LSCO) and Bi_2(Sr,La)_2CuO_{6+δ} (Bi2201), some experiments seem to indicate an onset of SC fluctuations at very high temperatures (2-3 times T_c^{max}, the T_c value at optimal hole concentration p), whereas other measurements suggest that fluctuations are confined to the immediate vicinity of T_c(p). Here we use torque magnetization to resolve this conundrum by systematically studying LSCO, Bi2201 and HgBa_2CuO_{4+δ} (Hg1201). The latter is a more ideal single-layer compound, featuring high structural symmetry, minimal disorder, and T_c^{max} = 97 K, a value more than twice those of LSCO and Bi2201. We find in all three cases that SC diamagnetism vanishes in an unusual exponential fashion above T_c, and at a rapid rate that is universal. Furthermore, the high characteristic fluctuation temperatures of LSCO and Bi2201 closely track T_c(p) of Hg1201. These observations suggest that, rather than being indicative of SC diamagnetism, the fluctuations at high temperatures in the low-T_c^{max} compounds are associated with a competing order. This picture is further supported by an analysis of available results for double-layer cuprates.