The superfluid density rho_s(T) = 1/lambda^2(T) has been measured at 2.64 GHz in highly underdoped YBCO, at 37 dopings with T_c between 3 K and 17 K. Within limits set by the transition width Delta T_c ~ 0.4 K, rho_s(T) shows no evidence of critical fluctuations as T goes to T_c, with a mean-field-like transition and no indication of vortex unbinding. Instead, we propose that rho_s displays the behaviour expected for a quantum phase transition in the (3 + 1)-dimensional XY universality class, with rho_s0 ~ (p - p_c), T_c ~ (p - p_c)^1/2 and rho_s(T) ~ (T_c - T)^1 as T goes to T_c.
@article{arxiv.cond-mat/0509223,
title = {Superfluid Density in a Highly Underdoped YBCO Superconductor},
author = {D. M. Broun and W. A. Huttema and P. J. Turner and S. Ozcan and B. Morgan and Ruixing Liang and W. N. Hardy and D. A. Bonn},
journal= {arXiv preprint arXiv:cond-mat/0509223},
year = {2015}
}