We report angle-resolved photoemission spectroscopy measurements of the excitation gap in underdoped superconducting thin films of ${\mathrm{Bi}}_2{\mathrm{Sr}}_2{\mathrm{Ca}}_{1-x}{\mathrm{Dy}}_x{\mathrm{Cu}}_2{\mathrm{O}}_{8+\delta }$. As $T_c$ is reduced by a factor of 2 by underdoping, the superconducting state gap $\Delta$ does not fall proportionally, but instead stays constant or increases slightly, in violation of the BCS mean-field theory result. The different doping dependences of $\Delta$ and $k{T}_c$ indicate that they represent different energy scales. The measurements also show that $\Delta$ is highly anisotropic and consistent with a $d_{x^2-y^2}$ order parameter, as in previous studies of samples with higher dopings. However, in these underdoped samples, the anisotropic gap persists well above $T_c$. The existence of a normal state gap is related to the failure of $\Delta$ to scale with $T_c$ in theoretical models that predict pairing without phase coherence above $T_c$.

• Received 30 July 1996

DOI:https://doi.org/10.1103/PhysRevB.54.R15665