Doping dependence of the low-energy excitations in superconducting Bi/sub 2/Sr/sub 2/CaCu/sub 2/O/sub 8+ delta /: evidence for thermal phase fluctuations

By using a single-coil technique, we study the low-temperature dependence of the in-plane magnetic penetration depth lambda /sub ab/ in several Bi/sub 2/Sr/sub 2/CaCu/sub 2/O/sub 8+ delta / (BSCCO) single crystals prepared with various doping levels delta ranging from the under- to the overdoped regime. Four samples exhibit a linear dependence of thermally activated low-energy excitations Delta lambda /sub ab/ identical to lambda /sub ab/(T)- lambda /sub ab/(0)~T. The thermal activation rate varies as delta lambda /sub ab// delta T is minimum, 8 AA/K, at optimum doping, in good quantitative agreement with the d-wave model of superconducting order parameter. The much larger rates, >or approximately=40 AA/K, observed in all under- and overdoped samples indicate that, in these samples, another type of low-energy excitations is relevant. These large rates are quantitatively consistent with a model of thermal phase fluctuations suitable for granular superconductors with short coherence length like cuprates. One underdoped sample exhibits a quadratic dependence suggesting an incipient crossover from thermal to quantum fluctuations.