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

The superfluid density ρ s (T) ≡ 1/λ 2 (T) has been measured at 2.64 GHz in highly underdoped YBa 2 Cu 3 O 6+v , at 37 dopings with T c between 3 and 17 K. Within limits set by the transition width ΔT c ≈ 0.4 K, ρ 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 ρ s displays the behavior expected for a quantum phase transition in the (3 +1)-dimensional XY universality class, with ρ s0 ∞ (p - p c ), T c ∞ (p - p c ) 1/2 , and ρ s (T) ∞ (T c -T) 1 as T → T c .