Specific-heat measurement of a residual superconducting state in the normal state of underdoped Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta} cuprate superconductors.

We have measured the magnetic field and temperature dependence of specific heat on Bi_{2}Sr_{2-x}La_{x}CuO_{6+delta} single crystals in wide doping and temperature regions. The superconductivity related specific-heat coefficient gamma_{sc} and entropy S_{sc} are determined. It is found that gamma_{sc} has a humplike anomaly at T_{c} 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 T_{c}. 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 T_{c}.