Specific-Heat Measurement of a Residual Superconducting State in the Normal State of UnderdopedBi2Sr2−xLaxCuO6+δCuprate Superconductors

We have measured the magnetic field and temperature dependence of specific heat on Bi2Sr2� xLaxCuO6þ� single crystals in wide doping and temperature regions. The superconductivity related specific-heat coefficientsc and entropy Ssc are determined. It is found thatsc has a humplike anomaly at Tc and behaves as a long tail which persists far into the normal state for the underdoped samples, but for the heavily overdoped samples the anomaly ends sharply just near Tc. Interestingly, we found that the entropy associated with superconductivity is roughly conserved when and only when the long tail part in the normal state is taken into account for the underdoped samples, indicating the residual superconductivity above Tc.