Gap distributions and spatial variation of electronic states in superconducting and pseudogap states of Bi₂Sr₂Ca₂CuO_8+δ

High-resolution scanning tunneling microscopy has been used to study the tunneling density of states in lightly underdoped samples of the high-T_c superconductor Bi₂Sr₂Ca₂CuO_8+δ in both the superconducting and pseudogap states. We demonstrate that the tunneling gaps observed in these two states have identical spatial distributions and correlation lengths. This observation suggests that the two gaps, and hence the two phenomena, cannot have a competing origin. In addition, we present measurements that show that in contrast to the superconducting state, in which low energy quasi-particles are homogenous in real space, the states near the Fermi level are spatially inhomogeneous in the pseudogap state. The variation of the low-energy electronic states is spatially correlated with local changes in the pseudogap.