Experimental evidence of paired hole states in model high-$T_c$ compounds

The distribution of holes in Sr$_{14-x}$Ca$_x$Cu$_{24}$O$_{41}$ (SCCO) is revisited with semi-emperical reanalysis of the x-ray absorption (XAS) data and exact-diagonalized cluster calculations. A new interpretation of the XAS data leads to much larger ladder hole densities than previously suggested. These new hole densities lead to a simple interpretation of the hole crystal (HC) recently reported with 1/3 and 1/5 wave vectors along the ladder. Our interpretation is consistent with paired holes in the rung of the ladders. Exact diagonalization results for a minimal model of the doped ladders suggest that the stabilization of spin structures consisting of 4 spins in a square plaquette as a result of resonance valence bond (RVB) physics suppresses the hole crystal with a 1/4 wave vector.