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We have measured the magnetic field and temperature dependence of specificheat on $Bi_2Sr_{2-x}La_xCuO_{6+\delta}$ single crystals in wide doping andtemperature regions. The superconductivity related specific heat coefficient$\gamma_{sc}$ and entropy $S_{sc}$ are determined. It is found that$\gamma_{sc}$ has a hump-like anomaly at $T_c$ and behaves as a long tail whichpersists far into the normal state for the underdoped samples, but for theheavily overdoped samples the anomaly ends sharply just near $T_c$.Interestingly, we found that the entropy associated with superconductivity isroughly conserved when and only the long tail part in the normal state is takeninto account for the underdoped samples, indicating the residualsuperconductivity above T$_c$.

Specific-Heat Measurement of Residual Superconductivity in the Normal State of Underdoped Cuprate Superconductors