Superfluid density in a highly underdoped YBa_{2}Cu_{3}O_{6+y} superconductor

The superfluid density rho_{s}(T) identical with1/lambda;{2}(T) has been measured at 2.64 GHz in highly underdoped YBa_{2}Cu_{3}O_{6+y}, at 37 dopings with T_{c} between 3 and 17 K. Within limits set by the transition width DeltaT_{c} approximately 0.4 K, rho_{s}(T) shows no evidence of critical fluctuations as T-->T_{c}, with a mean-field-like transition and no indication of vortex unbinding. Instead, we propose that rho_{s} displays the behavior expected for a quantum phase transition in the (3+1)-dimensional XY universality class, with rho_{s0} proportional, variant(p-p_{c}), T_{c} proportional, variant(p-p_{c});{1/2}, and rho_{s}(T) proportional, variant(T_{c}-T);{1} as T-->T_{c}.