High Field Phase Diagram of Cuprates Derived from the Nernst Effect

Measurements of the Nernst signal in the vortex-liquid state of the cuprates to high fields (33 T) reveal that vorticity extends to very high fields even close to the zero-field critical temperature $T_{c0\mathrm{}}$. In overdoped ${\mathrm{La}}_{2-x}{\mathrm{Sr}}_x{\mathrm{CuO}}_4$, we show that the upper critical field $H_{c2\mathrm{}}\left(T\right)$ curve does not end at $T_{c0\mathrm{}}$, but at a much higher temperature. These results imply that $T_{c0\mathrm{}}$ corresponds to a loss in phase rigidity rather than a vanishing of the pairing amplitude. An intermediate field $H^{*}\left(T\right)\ll H_{c2\mathrm{}}\left(T\right)$ is shown to be the field scale for the flux-flow resistivity.