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Absence of gross inhomogeneity in HTS cuprates

Recent scanning tunnelling microscopy (STM) studies on Bi$_2$Sr$_2$CaCu$_2$O$_{8+δ}$ (Bi-2212) revealed the presence of severe inhomogeneity with length scale $L_0 \approx ξ_0$, the coherence length. Other studies have been interpreted in terms of mesoscale or nanoscale phase segregation. Here we analyze heat capacity and NMR data on Bi-2212 and (Y,Ca)Ba$_2$Cu$_3$O$_{7-δ}$ and find no evidence for phase segregation or gross inhomogeneity. For Bi-2212 the coherence scale $L_0$ increases with doping from 5 to 17$ξ_0$ and the hole density inhomogeneity decreases from 0.028 to 0.005 holes/Cu. We conclude that STM measurements considerably overstate the inhomogeneity in bulk Bi-2212.