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Evidence of two-dimensional (2D) quantum critical fluctuations is observed inthe superfluid density ns(T) \propto $\lambda$ -2(T) of deeply underdopedBi2Sr2CaCu2O8+x (Bi-2212) films, indicating that quantum fluctuations play adominant role in underdoped cuprates in general. 2D fluctuations are expressedby the linear scaling, Tc \propto ns(0). 2D scaling in Bi-2212 contrasts with3D scaling seen in the much less anisotropic YBa2Cu3O7-x. Quantum criticalfluctuations could also account for the absence of thermal critical behavior in\lambda^{-2}(T) of strongly underdoped Bi-2212 samples, Tc < 48 K.

Evidence of Two-Dimensional Quantum Critical Behavior in the Superfluid Density of Deeply Underdoped Bi2Sr2CaCu2O8+x