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Thermodynamic critical field curves have been measured for$La_{2-x}Sr_{x}CuO_{4+\delta}$ over the full range of carrier concentrationswhere superconductivity occurs in order to determine changes in the normalstate density of states with carrier concentration. There is a substantialwindow in the $H-T$ plane where the measurements are possible because thesamples are both thermodynamically reversible and the temperature is low enoughthat vortex fluctuations are not important. In this window, the data fitHao-Clem rather well, so this model is used to determine $H_c$ and $\kappa_c$for each temperature and carrier concentration. Using N(0) and the ratio of theenergy gap to transition temperature, $\Delta (0)/k_BT_c$, as fittingparameters, the $H_c vs T$ curves give $\Delta (0)/k_BT_c \sim 2.0$ over thewhole range of $x$. Values of N(0) remain rather constant in the optimum-dopedand overdoped regime, but drops quickly toward zero in the underdoped regime.

physical review. b, condensed matter

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