Magnetic properties of type-II superconductors with reduced phase stiffness

Motivated by the phenomenology of underdoped cuprates, we study a modified Ginzburg-Landau theory which describes type-II superconductors with reduced phase stiffness. The theory is characterized by three length scales: the penetration depth, lambda, the amplitude coherence length, xi, and the phase coherence length, xi(perpendicular to). Within the modified theory, we solve the single-vortex problem and calculate both, the lower and the upper critical fields H-c1 and H-c2. We also present an approximate calculation of the equilibrium magnetization curve M=M(H). Our results explain the difference in scaling of lambda(-2) and H-c1 with the doping level in underdoped cuprates. Further experimental tests of our theory are proposed.