Lower Critical Field and Superfluid Density of Highly Underdoped YBa₂Cu₃O_6+x Single Crystals
Ruixing Liang, D.A. Bonn, W.N. Hardy, and David Broun
Published in Phys. Rev. Lett. 94, 117001 (2005).

The lower critical field H_c1 for highly underdoped YBa₂Cu₃O_6+x with T_c between 8.9 and 22 K has been determined by measurements of magnetization M(H) curves with applied field parallel to the c axis. H_c1 is linear in temperatures below about 0.6T_c, and H_c1(0) is proportional to T_c^{1.64 ± 0.04}, clearly violating the proportionality between rho_s(0) and T_c. Moreover, the slope -dH_c1/dT decreases steeply toward zero as T_c approaches zero, indicating that the effective charge of the quasiparticles vanishes as the doping is decreased toward the insulating phase.