Magnetization, Nernst effect and vorticity in the cuprates

Nernst and magnetization experiments reveal the existence of a large region of the cuprate phase diagram above the $T_c$ curve in which vorticity and weak diamagnetism exist without phase coherence. We discuss the implication that the transition at $T_c$ is caused by the loss of long-range phase coherence caused by spontaneous vortex creation. Below $T_c$, these measurements provide an estimate of the depairing field $H_c2$ which is found to be very large (40-100 T depending on doping). We discuss the high-field Nernst and magnetization results, binding energy, and the phase diagram of hole-doped cuprates. Some new magnetization results on the vortex liquid in very underdoped LSCO in the limit $T\to 0$ are reported as well.