Anomalous superconducting state gap size versus behavior in underdoped

We report angle-resolved photoemission spectroscopy measurements of the excitation gap in underdoped superconducting thin films of (Formula presented). As (Formula presented) is reduced by a factor of 2 by underdoping, the superconducting state gap (Formula presented) 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 (Formula presented) and (Formula presented) indicate that they represent different energy scales. The measurements also show that (Formula presented) is highly anisotropic and consistent with a (Formula presented) order parameter, as in previous studies of samples with higher dopings. However, in these underdoped samples, the anisotropic gap persists well above (Formula presented). The existence of a normal state gap is related to the failure of (Formula presented) to scale with (Formula presented) in theoretical models that predict pairing without phase coherence above (Formula presented).