Superfluid density in a highly underdoped YBa2Cu3O6+y superconductor

The superfluid density rho(s)(T)equivalent to 1/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 Delta T(c)approximate to 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 to(p-p(c)), T(c)proportional to(p-p(c))(1/2), and rho(s)(T)proportional to(T(c)-T)(1) as T -> T(c).